具有分数阶线性记忆的非经典反应扩散方程解的渐近性

The Asymptotic Behavior of Solutions for a Class of NonclassicalReaction-Diffusion Equations withFractional Linear Memory

研究了一类具有分数阶线性记忆的非经典反应扩散方程解的渐近性行为. 定义合适的 Lyapunov 泛函, 证明了当非线性项f满足增长性条件, 记忆核g呈指数衰减时,系统的解是多项式衰减的;随后, 应用半群理论, 证明了解是非指数稳定的.

The asymptotic behavior of solutions for a class of nonclassical reaction-diffusion e-quations with fractional linear memory is investigated. by defining an appropriate Lyapunov functional, it is proved that the solution of the system decays polynomially when the nonlinear term f satisfies the growth condition and the memory kernel g decays exponentially. After that, we achieve that the solution is non-exponentially stable by means of the semigroup theory.