Uniform tail estimates and $ L^p( {\mathbb{R}}^N) $-convergence for finite-difference approximations of nonlinear diffusion equations
Uniform tail estimates and $ L^p( {\mathbb{R}}^N) $-convergence for finite-difference approximations of nonlinear diffusion equations
We obtain new equitightness and $C([0,T];L^p(\mathbb{R}^N))$-convergence results for finite-difference approximations of generalized porous medium equations of the form $$ \partial_tu-\mathfrak{L}[\varphi(u)]=g\qquad\text{in $\mathbb{R}^N\times(0,T)$}, $$ where $\varphi:\mathbb{R}\to\mathbb{R}$ is continuous and nondecreasing, and $\mathfrak{L}$ is a local or nonlocal diffusion operator. Our results include slow diffusions, strongly degenerate Stefan problems, and fast diffusions above …