Reaction-diffusion in irregular domains
The paper deals with the Cauchy-Dirichlet and Dirichlet problems for the reaction-diffusion equation which is a degenerate nonlinear parabolic one. The problems are considered in noncylindrical domains with nonsmooth boundaries. Under some restrictions existence, uniqueness and comparison theorems for generalized solutions are proved. The constructed solutions are continuous up to the nonsmooth boundary if at each interior point the left modulus of the lower (respectively upper) semicontinuity of the left (respectively right) boundary curve satisfies an upper (respectively lower) Hölder condition near zero with Hölder exponent \(\nu >1/2\).
scientific article; zbMATH DE number 1515446
scientific article