具有混合乘积型非线性的阻尼波动系统的临界阈值
Critical thresholds for the damped wave system with mixed product-type nonlinearities
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中文总结 AI 辅助
本文确定了具有混合乘积型非线性的阻尼波动耦合系统柯西问题中，小幅数据温和解全局存在与不存在的临界曲线，并首次给出此类系统的临界阈值结果。
中文摘要 AI 辅助
本文研究了一类具有混合乘积型非线性的阻尼波动方程耦合系统的柯西问题。我们成功地确定了以非线性项的幂指数表述的临界曲线，该曲线刻画了小幅数据温和解的全局（时间）存在性与全局温和解的不存在性。此外，全局存在性结果通过Schauder不动点定理和Banach压缩映射原理建立，而不存在性分析则依赖于一种适应于非线性项乘积型结构的新迭代格式。据我们所知，这项工作首次为此类系统提供了临界阈值结果。
英文摘要
In this paper, we study the Cauchy problem for a coupled system of damped wave equations with mixed product-type nonlinearities. We have succeeded in determining the critical curve, formulated in terms of the power exponents of nonlinearities, for the global (in time) existence of small data mild solutions and the nonexistence of global mild solutions. Moreover, the global existence result is established by means of Schauder's fixed point theorem and Banach's contraction principle, whereas the nonexistence analysis relies on a new iteration scheme adapted to the product-type structure of nonlinearities. To the best of our knowledge, this work provides the first critical threshold results for such systems.
