Existence and Uniqueness of Solutions to Nonlinear Diffusion with Memory

Yixian Chen

This paper studies a nonlinear diffusion equation with memory: $$u_t=\nabla \cdot (D(x)\cdot {\int }_0^{t}K(t-s)\nabla \cdot \hat{I}¦(u(x,s))ds)+f(x,t)$$ Where $K$ is memory Kernel an…