论文标题
反应的多孔介质方程溶液的收敛
Convergence of Solutions of the Porous Medium Equation with Reactions
论文作者
论文摘要
考虑具有反应的一维多孔培养基方程（PME）的库奇问题。我们首先证明了一般的收敛结果，即，以非负紧密支持的初始数据为$ t \ to \ infty $开始的任何有界的全局解决方案，将反应项的非负零或基态固态固定解决方案收敛。基于它，我们对PME解决方案的渐近行为进行了完整的分类，具有单稳态，可动和燃烧类型的非线性类型。
Consider the Cauchy problem of one dimensional porous medium equation (PME) with reactions. We first prove a general convergence result, that is, any bounded global solution starting at a nonnegative compactly supported initial data converges as $t\to \infty$ to a nonnegative zero of the reaction term or a ground state stationary solution. Based on it, we give out a complete classification on the asymptotic behaviors of the solutions for PME with monostable, bistable and combustion types of nonlinearities.
