Reaction–Diffusion in Irregular Domains
Reaction–Diffusion in Irregular Domains
复制标题
不规则区域中的反应扩散
DOI：
10.1006/jdeq.2000.3761
复制
发表时间：
2000
影响因子：
2.4
通讯作者：
U. Abdulla
中科院分区：
文献类型：
--
作者：
U. Abdulla
Abstract We consider the Cauchy–Dirichlet and Dirichlet problems for the nonlinear parabolic equation u t − a ( u m ) xx + bu β =0,where a >0, b ∈ R 1 , m >0, and β >0. The problems are considered in noncylindrical domains with nonsmooth boundaries. Existence, uniqueness, and comparison results are established. 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) Holder condition near zero with Holder exponent ν > 1 2 . The value 1 2 is critical as in the classical theory of the heat equation u t = u xx .
