Convergence of solutions to the degenerate reaction diffusion equation with Dirichlet boundary condition
We consider the asymptotic behavior of solutions to the porous medium equation with a positive bistable type reaction term and Dirichlet boundary condition.We first prove a convergence result.Furthermore,by investigating families of initial data of the type {φσ}σ＞0,where φσ belongs to an appropriate class of nonnegative compactly supported functions,we prove small spreading-big spreading dichotomy on the asymptotic behavior of the solutions.
porous medium equationDirichlet boundary conditionasymptotic behavior
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