论文标题
与一般非线性记忆项的半线性波方程的弱耦合系统爆炸的相互作用影响
Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms
论文作者
论文摘要
在本文中，我们研究了具有一般形式的不同非线性记忆项的半线性波方程的弱耦合系统，以及具有一般非线性记忆项的相应单线性方程。多亏了Banach的固定点定理，我们证明了在内存内核上具有$ l^1 $假设的解决方案的存在。然后，通过使用与切片程序相关的迭代方法得出能量溶液的爆炸结果。我们研究了记忆项上不同减少假设下的爆破条件的相互作用。特别是，找到了互动效应的内核的新阈值。此外，我们在半线性波方程和声波方程中提供了一些结果的应用。
In this paper, we study weakly coupled systems for semilinear wave equations with distinct nonlinear memory terms in general forms, and the corresponding single semilinear equation with general nonlinear memory terms. Thanks to Banach's fixed point theorem, we prove local (in time) existence of solutions with the $L^1$ assumption on the memory kernels. Then, blow-up results for energy solutions are derived applying iteration methods associated with slicing procedure. We investigate interactions on the blow-up conditions under different decreasing assumptions on the memory term. Particularly, a new threshold for the kernels on interplay effect is found. Additionally, we give some applications of our results on semilinear wave equations and acoustic wave equations.
