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Global existence and nonexistence of solutions for coupled nonlinear wave equations with damping and source terms

Yaojun Ye
대한수학회 (The Korean Mathematical Society)|2014.11|대한수학회보 (Bulletin of the KMS)|제51권 제6호|pp. 1697-1710

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키워드

blow-upsystems of nonlinear wave equationsdamping and source termsglobal solutionslifespan of solutions
주제분류수학

초록

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

Abstract

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

참고문헌 (15)

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  10. B. Said-Houari, "Global nonexistence of positive initial-energy solutions of a system of nonlinear wave equations with damping and source terms", Differential Integral Equations, 23(1-2), pp.79~92 (2010)
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관련 논문AI추천

GLOBAL EXISTENCE AND UNIFORM DECAY OF COUPLED WAVE EQUATION OF KIRCHHOFF TYPE IN A NONCYLINDRICAL DOMAIN하태갑대한수학회 · 대한수학회지2017 · 제54권 제4호Global nonexistence for the wave equation with boundary variable exponent nonlinearities박선혜, 하태갑대한수학회 · 대한수학회지2022 · 제59권 제1호Blow-up rate for the semi-linear wave equation in bounded domainChuangchuang Liang, Pengchao Wang대한수학회 · 대한수학회보2015 · 제52권 제1호Blow-up of solutions for wave equations with strong damping and variable-exponent nonlinearity박선혜대한수학회 · 대한수학회지2021 · 제58권 제3호Global Nonexistence of Solutions for a Quasilinear Wave Equation with Time Delay and Acoustic Boundary Conditions강용한, 박종열경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제4호Global solutions for a class of nonlinear sixth-order wave equationYing Wang대한수학회 · 대한수학회보2018 · 제55권 제4호

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