Abstract

An initial-boundary value problem posed on a bounded interval is considered for a class of odd-order (more than one) quasilinear evolution equations with general nonlinearity. Assumptions on the equations do not provide global a priori estimates for solutions of an arbitrary size. For small initial and boundary data, small right-hand side function results on global existence and uniqueness of small weak solutions, as well as on their large-time exponential decay are established.

中文翻译：

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有界区间上具有一般非线性的奇数阶拟线性演化方程

摘要

对于一类具有一般非线性的奇数阶（多于一个）拟线性演化方程，考虑在有界区间上提出的初始边界值问题。方程的假设不提供任意大小的解的全局先验估计。对于小的初始和边界数据，建立了小弱解的全局存在性和唯一性以及它们的大时间指数衰减的小右手边函数结果。