具有非线性广义源项和应力项的变系数波动方程解的整体存在性与不存在性
The Global Existence and Nonexistence of Solutions for the Variable Coefficient Wave Equation with Nonlinear Generalized Source Term and Stress Term
摘要: 本文主要研究了一类含应力项的非线性变系数波动方程在不同能级下解的整体存在性及其爆破行为。基于泛函估计方法，构建了位势井框架，并在此基础上给出了次临界能级下解全局存在的条件及其解的爆破时间估计。同时，还探讨了临界能级下全局解存在的条件。
Abstract: This paper mainly studies the existence of global solutions and the blow-up behavior for a class of nonlinear variable coefficient wave equations with stress term under different energy levels. Based on functional estimates, the potential well framework is constructed, and the conditions for the existence of global solutions and blow-up time under subcritical energy levels are provided. Additionally, the conditions for the existence of global solutions at the critical energy level are discussed.
文章引用：于佳利, 魏天莹. 具有非线性广义源项和应力项的变系数波动方程解的整体存在性与不存在性[J]. 应用数学进展, 2025, 14(1): 112-125. https://doi.org/10.12677/aam.2025.141015

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