Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source

Abstract EN

This paper is concerned with a nonlocal nonlinear diffusion equation with Dirichlet boundary condition and a source ut(x,t)=∫-∞+∞J((x-y)/u(y,t))dy-u(x,t)+up(x,t), x∈(-L,L), t>0, u(x,t)=0, x∉(-L,L), t≥0, and u(x,0)=u0(x)≥0, x∈(-L,L), which is analogous to the local porous medium equation.

First, we prove the existence and uniqueness of the solution as well as the validity of a comparison principle.

Next, we discuss the blowup phenomena of the solution to this problem.

Finally, we discuss the blowup rates and sets of the solution.