SU\G(𝔸)/K·U
Mathematics › Modeling and Simulation

Mathematical Biology Tumor Growth

Works Count: 26815

Description

This cluster of papers focuses on the mathematical modeling of cancer growth, tumor invasion, and treatment strategies. It covers topics such as chemotaxis, angiogenesis, cellular automaton models, multiscale modeling, drug therapy, and interactions between the immune system and tumors.

Keywords

Mathematical Modeling; Cancer Growth; Tumor Invasion; Chemotaxis; Angiogenesis; Cellular Automaton; Multiscale Model; Drug Therapy; Immune System Interactions; Tumor Dynamics

Most Cited Works

Action Title Date Authors
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Dynamics of Evolutionary Equations 2002-01-01 George R. Sell Yuncheng You
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Transport Equations in Biology 2006-12-14 Benoı̂t Perthame
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The Clonal Evolution of Tumor Cell Populations 1976-10-01 Peter C. Nowell̀
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Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems 2004-02-06 David Angeli James E. Ferrell Eduardo D. Sontag
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Spatial segregation of interacting species 1979-07-01 Nanako Shigesada Kohkichi Kawasaki Ei Teramoto
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Traveling bands of chemotactic bacteria: A theoretical analysis 1971-02-01 Evelyn Fox Keller Lee A. Segel
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Cancer Stem Cells: Impact, Heterogeneity, and Uncertainty 2012-03-01 Jeffrey A. Magee Elena Piskounova Sean J. Morrison
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The Gradient-Sensing Mechanism in Bacterial Chemotaxis 1972-09-01 Robert M. Macnab Daniel E. Koshland
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A user’s guide to PDE models for chemotaxis 2008-07-14 Thomas Hillen Kevin J. Painter
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Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model 2010-02-22 Michael Winkler
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Stability analysis of swarms 2003-04-01 Veysel Gazi Kevin M. Passino
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A Big Bang model of human colorectal tumor growth 2015-02-09 Andrea Sottoriva Haeyoun Kang Zhicheng Ma Trevor A. Graham Matthew P. Salomon Junsong Zhao Paul Marjoram Kimberly D. Siegmund Michael F. Press Darryl Shibata
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The Importance of Being Discrete (and Spatial) 1994-12-01 Rick Durrett Simon A. Levin
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The approach of solutions of nonlinear diffusion equations to travelling front solutions 1977-12-01 Paul C. Fife J. B. McLeod
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Model for chemotaxis 1971-02-01 Evelyn Fox Keller Lee A. Segel
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Physics of chemoreception 1977-11-01 Howard C. Berg Edward M. Purcell
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Kinetics of vascular normalization by VEGFR2 blockade governs brain tumor response to radiation 2004-12-01 Frank Winkler Sergey V. Kozin Ricky T. Tong Sung‐Suk Chae Michael F. Booth Igor Garkavtsev Lei Xu Daniel J. Hicklin Dai Fukumura Emmanuelle di Tomaso
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Influence of tumour micro-environment heterogeneity on therapeutic response 2013-09-17 Melissa R. Junttila FrĂŠdĂŠric J. de Sauvage
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Cell and Environment Interactions in Tumor Microregions: The Multicell Spheroid Model 1988-04-08 Robert M. Sutherland
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Nonlinear Aspects of Competition Between Three Species 1975-09-01 Robert M. May Warren J. Leonard
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Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis 1998-09-01 Alexander R.A. Anderson
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Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues 2015-03-25 Nicola Bellomo Abdelghani Bellouquid Yixin Tao Michael Winkler
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Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos 1974-11-15 Robert M. May
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Some properties of viscosity solutions of Hamilton-Jacobi equations 1984-01-01 Michael G. Crandall L. C. Evans Pierre‐Louis Lions
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Nonlocal Operators with Applications to Image Processing 2008-11-12 Guy Gilboa Stanley Osher
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Cancer heterogeneity: implications for targeted therapeutics 2013-01-08 Rosalie Fisher Lajos Pusztai Charles Swanton
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Ultrasensitivity in the mitogen-activated protein kinase cascade. 1996-09-17 Chi‐Ying F. Huang James E. Ferrell
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Chemotaxis in Escherichia coli analysed by Three-dimensional Tracking 1972-10-01 Howard C. Berg Douglas A. Brown
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Stochasticity in Transcriptional Regulation: Origins, Consequences, and Mathematical Representations 2001-12-01 Thomas B. Kepler Timothy C. Elston
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Active contours without edges 2001-01-01 Tony F. Chan Luminita A. Vese
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Patient-Derived Xenograft Models: An Emerging Platform for Translational Cancer Research 2014-07-16 Manuel Hidalgo FrĂŠdĂŠric Amant Andrew V. Biankin Eva BudĂ­nskĂĄ Annette T. Byrne Carlos Caldas Robert B. Clarke Steven de Jong Jos Jonkers Gunhild M. MĂŚlandsmo
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Biomimicry of bacterial foraging for distributed optimization and control 2002-06-01 Kevin M. Passino
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Cancer as an evolutionary and ecological process 2006-11-16 Lauren M.F. Merlo John W. Pepper Brian J. Reid Carlo C. Maley
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Stochastic State Transitions Give Rise to Phenotypic Equilibrium in Populations of Cancer Cells 2011-08-01 Piyush B. Gupta Christine M. Fillmore Guozhi Jiang Sagi Shapira Kai Tao Charlotte Kuperwasser Eric S. Lander
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Robust perfect adaptation in bacterial chemotaxis through integral feedback control 2000-04-25 Tau‐Mu Yi Yun Huang Melvin I. Simon John C. Doyle
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Robustness of Cellular Functions 2004-09-01 JĂśrg Stelling Uwe Sauer ZoltĂĄn SzĂĄllĂĄsi Francis J. Doyle John C. Doyle
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Random walk models in biology 2008-04-15 Edward A. Codling Michael J. Plank Simon Benhamou
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Maintenance Therapy With Tumor-Treating Fields Plus Temozolomide vs Temozolomide Alone for Glioblastoma 2015-12-15 Roger Stupp Sophie Taillibert Andrew A. Kanner Santosh Kesari David M. Steinberg Steven A. Toms Lynne P. Taylor Frank S. Lieberman Antonio Silvani Karen Fink
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Controlled markov processes and viscosity solutions 1994-07-01 M. R. James
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Rindopepimut with temozolomide for patients with newly diagnosed, EGFRvIII-expressing glioblastoma (ACT IV): a randomised, double-blind, international phase 3 trial 2017-08-23 Michael Weller Nicholas Butowski David Tran Lawrence D. Recht Michael Lim Hal W. Hirte Lynn S. Ashby Laszlo Mechtler Samuel Goldlust FĂĄbio M. Iwamoto
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Current and future perspectives of liquid biopsies in genomics-driven oncology 2018-11-08 Ellen Heitzer Imran S. Haque Charles E. S. Roberts Michael R. Speicher
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Organoid Modeling of the Tumor Immune Microenvironment 2018-12-01 James T. Neal Xingnan Li Junjie Zhu Valeria GiangarrĂ  Caitlin L. Grzeskowiak Jihang Ju Iris H. Liu Shin-Heng Chiou Ameen A. Salahudeen Amber R. Smith
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An Integrative Model of Cellular States, Plasticity, and Genetics for Glioblastoma 2019-07-18 Cyril Neftel Julie Laffy Mariella G. Filbin Toshiro Hara Marni E. Shore Gilbert J. Rahme Alyssa Richman Dana Silverbush McKenzie Shaw Christine Hebert
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Mathematical Problems in Image Processing 2006-01-01 Gilles Aubert Pierre Kornprobst
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Evolutionary Integral Equations and Applications 1993-01-01 Pruss Jan
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The Kinetics of Cellular Proliferation 1960-10-01
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Variational Analysis 1998-01-01 R. T. Rockafellar Roger J.‐B. Wets
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Nodal Discontinuous Galerkin Methods 2007-12-19 Jan S. Hesthaven Tim Warburton
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Optimal Control of Systems Governed by Partial Differential Equations 1971-01-01 J. L. Lions
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A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate. 1979-11-01 Goldie Jh Coldman Aj

Most Recent Works

Action Title Date Authors
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Parameter Estimation of a Tumor Growth Model under Data-driven Approach and Its Numerical Solution in Matlab 2025-04-28 Zhuo Chen Yi Zeng Wei Chen Ruixian Zheng Z. Z. Du Meibao Ge
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A novel model of glioblastoma recurrence to identify therapeutic vulnerabilities 2025-04-28 Sara Lucchini James Nicholson Xinyu Zhang Jacob Househam Yau Mun Lim Maximilian Mossner Thomas O Millner Sebastian Brandner Trevor A. Graham Silvia Marino
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Predictive modeling of glioblastoma recurrence for therapeutic target identification 2025-04-28 Hrvoje Miletić Thomas Daubon
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Chaos and its control in a discretized fractional order tumor-immune system Model with benign and malignant case 2025-04-28 Fuat Gürcan Şenol Kartal
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Observer-based boundary control for semi-linear stochastic systems 2025-04-29 R. Ragul K. Mathiyalagan
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A Diffusive Predator-Prey System with a Free Boundary 2025-04-29 M. S. Rasulov Sh.M. Jamoldinova
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Adaptive Therapy Exploits Fitness Deficits in Chemotherapy-Resistant Ovarian Cancer to Achieve Long-Term Tumor Control 2025-04-29 Helen Hockings Eszter Lakatos Weini Huang Maximilian Mossner Ateeb Khan Nikolina Bakali Jacqueline McDermott Kane Smith Ann‐Marie Baker Trevor A. Graham
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Finite-time blow-up on a volume-filling attraction–repulsion system 2025-04-29 Chang-Jian Wang Xincai Zhu Chun‐Xia He
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Biological aggregations from spatial memory and nonlocal advection 2025-04-29 Di Liu Jonathan R. Potts Yurij Salmaniw Junping Shi Hao Wang
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Weak measure expansive symplectic systems 2025-04-29 Manseob Lee Jumi Oh
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Bayesian Inference of Phenotypic Plasticity of Cancer Cells Based on Dynamic Model for Temporal Cell Proportion Data 2025-04-29 Shuli Chen Yuman Wang Da Zhou Jie Hu
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An Unconditionally Energy-Stable Sav-Dg Numerical Scheme for Tumor Growth Model 2025-04-29 Penghao Guo Bo Wang null Guang‐an Zou
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Stochastic modeling and first-passage-time analysis of oncological time metrics with dynamic tumor barriers 2025-04-29 Olusegun Michael Otunuga
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Propagation of Single-Species Models with Resource-Dependent Dispersal and Free Boundaries 2025-04-30 Dawei Zhang Yun Huang Chufen Wu
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Optimal Control of Forest Population System with Size Structure in Polluted Environment 2025-04-30 Fenghui Qin Zhanping Wang
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Stationary periodic patterns in a model of growing population of motile bacteria 2025-05-01 Valentina Bucur Bakhtier Vasiev
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Colony context and size-dependent compensation mechanisms give rise to variations in nuclear growth trajectories 2025-05-01 Julie C. Dixon Christopher L. Frick Chantelle L. Leveille Philip Garrison P. Lee Saurabh S. Mogre Benjamin Morris Nivedita Nivedita Ritvik Vasan Jianxu Chen
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Generation of a Three-Dimensional Spheroid Model of Tumor Cell Invasion 2025-04-28
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Numerical Investigation based on the Chebyshev-Homotopy Perturbation Method for the Breast Cancer as a Mathematical Model 2025-05-01 Mohamed Adel M. M. Khader Mohammed Messaoudi
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Vision transformer-based model can optimize curative-intent treatment for patients with recurrent hepatocellular carcinoma 2025-05-01 Ke Zhang Jinyu Ru Wenbo Wang Qiuping Ma Fengwei Gao Jiapeng Wu Zhifei Dai Qingyun Xie Lei Mu Haoyan Zhang
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Falsifying computational models of endothelial cell network formation through quantitative comparison with in vitro models. 2025-04-30 Tessa Vergroesen Vincent Vermeulen Roeland M. H. Merks
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A phase field model of Cahn–Hilliard type for tumour growth with mechanical effects and damage 2025-05-01 G. Cavalleri
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Global Boundedness of an Alarm–Taxis System With Nonlinear Diffusion 2025-05-02 Yue Zhou Changchun Liu
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Global boundedness in a chemotaxis-growth system with weak singular sensitivity in any dimensional setting 2025-05-04 Minh Le Halil Ä°brahim Kurt
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Chaos and Proportional Integral Derivative (PID) Control on Cancer Dynamics with Fractal fractional Operator 2025-05-01 Muhammad Farman Kottakkaran Sooppy Nisar Khadija Jamil Ali AkgĂźl Aceng Sambas Mustafa Bayram Mustafa Habib Murad Khan Hassani
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Stochastic pharmacodynamics of a heterogeneous tumour-cell population 2025-05-05 Van Thuy Truong Paolo Vicini James Yates Vincent F. S. Dubois Grant Lythe
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Generalizable AI predicts immunotherapy outcomes across cancers and treatments 2025-05-05 Wan Xiang Shen Thinh H. Nguyen Michelle M. Li Yepeng Huang Intae Moon Nitya Nair Daniel Marbach Marinka Žitnik
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Deformations of acid-mediated invasive tumors in a model with Allee effect 2025-05-05 Paul Carter Arjen Doelman Peter van Heijster David LĂŠvy Philip K. Maini Erin Okey Paige Yeung
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Numerical simulations of wave patterns in a stochastic partial differential equation model of tumor growth and invasion 2025-05-05 M.B.A. Mansour Hussien S. Hussien Asmaa H. Abobakr
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Similarity Solutions of Partial Differential–Integral Equations from the Theory of Stochastic Processes 2025-05-05 Mario Lefebvre
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On the fast signal limit in a chemotaxis system involving a tensor-valued sensitivity 2025-05-06 Jianzhong Wu Yinuo Han Qian Zhang
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Global Attraction of Age-Structured Population Models with Diffusion: Reduction of Dimension 2025-05-06 Alfonso Ruiz-Herrera Tarik Mohammed Touaoula
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The role of the toxin effect in the predator-prey system with prey-taxis 2025-05-01 Guiling Wu Jingyu Li Lu Xu
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On a parabolic-elliptic system of chemotaxis with logistic source and non-constant chemotactic coefficient 2025-05-06 J. Ignacio Tello
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Robust Analysis of Perturbed Backward Doubly Stochastic Differential Equations 2025-05-06 Jasmina Đorđević
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Ratio of T-cell Subsets Predicts Prognosis in Triple-Negative Breast Cancer Patients 2025-05-06 Pankaj Tyagi Dong‐Gun Lee Bernett Lee Siddhartha Mitra Jabed Iqbal
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Geometric aspects of bifurcations for a classical predator-prey model 2025-05-06 Wei Su Xiang Zhang
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Boundedness in a one-dimensional quasilinear attraction–repulsion chemotaxis system with flux limitation 2025-05-05 Yutaro Chiyo Kazuki Hasegawa Shohei Kohatsu Tomomi Yokota
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SAT-098 Infiltration of CD69- T cells in tumor tissue reflects longer recurrence-free survival in surgically resected hepatocellular carcinoma 2025-05-01 Pil Soo Sung Gil Won Lee Mi Hyun Kwon Kwon Yong Tak Seung Kew Yoon
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Global existence, boundedness and large time behavior for a chemotaxis model with singular sensitivity and nonlinear signal production 2025-05-01 Jing Zhang Chunlai Mu Xinyu Tu
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Optimal fractionation scheme for lymphocyte infiltration in glioblastoma multiforme radiotherapy 2025-05-08 Lorea Iturri Cristèle Gilbert Julie Espenon Annaïg Bertho Sarah Potiron Marjorie Juchaux Yolanda Prezado
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Global Existence and Mean-Field Limit for A Stochastic Interacting Particle System of Signed Coulomb Charges 2025-05-08 Patrick Meurs Mark A. Peletier Thomas Slangen
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Stretch and flow at the gliovascular interface: high-fidelity modelling of the mechanics of astrocyte endfeet 2025-05-08 Marius Causemann Rune Enger Marie E. Rognes
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Backward Bifurcation of an Age-Structured Epidemic Model with Partial Immunity 2025-05-08 Liming Cai Minghai Lei Jin Wang
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Deriving a suitable schedule through robust <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">H</mml:mi><mml:mi mathvariant="bold-italic">∞</mml:mi></mml:msub></mml:mrow></mml:math> and sliding mode control methods for cancer treatment using chemotherapy &amp; anti-angiogenic drugs 2025-05-09 Mostafa Solgi Hamed Moradi
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Lotka-Voterra competition model with nonlocal coefficient diffusion 2025-05-09 Marcos Antonio Viana Costa Cristian Morales-Rodrigo AntĂłnio SuĂĄrez
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Global existence of classical solutions of a two-species chemotaxis-competition system with consumption or linear signal production on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math> 2025-05-09 Weiyi Zhang Zuhan Liu
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Kolmogorov Equation for a Stochastic Reaction–Diffusion Equation with Multiplicative Noise 2025-05-09 K Guan Yu Shi
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A variational principle of the nonlinear Schrodinger equation with fractal derivatives 2025-05-09 Wenlei Li S. S. Chen Kang‐Jia Wang
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Global and exponential stabilization of a chemotactic alopecia areata model with signal-dependent diffusion and sensitivity 2025-05-10 Jing Zhang Shengmao Fu