Fundamental solutions for parabolic equations and systems: universal existence, uniqueness, representation
Fundamental solutions for parabolic equations and systems: universal existence, uniqueness, representation
In this paper, we develop a universal, conceptually simple and systematic method to prove well-posedness to Cauchy problems for weak solutions of parabolic equations with non-smooth, time-dependent, elliptic part having a variational definition. Our classes of weak solutions are taken with minimal assumptions. We prove the existence and uniqueness of …