Global well-posedness for nonlinear wave equations with supercritical source and damping terms

被引：3
作者：
Guo, Yanqiu
机构：
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 477卷 / 02期
关键词：
Nonlinear wave equations; Supercritical; Source terms; Damping; Global well-posedness; BLOW-UP; NONEXISTENCE THEOREMS; HYPERBOLIC EQUATION; EVOLUTION-EQUATIONS; WEAK SOLUTIONS; CAUCHY-PROBLEM; SYSTEMS; BOUNDARY; VISCOELASTICITY; ANALYTICITY;
D O I：
10.1016/j.jmaa.2019.05.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the global well-posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three-dimensional torus T-3 of the prototype u(tt) - Delta u + vertical bar u(t)vertical bar(m-1)u(t) = vertical bar u vertical bar(p-1)u, (x, t) is an element of T-3 x R+; u(0) = u(0) is an element of H-1 (T-3) boolean AND Lm+1(T-3), u(t)(0) = u(1) is an element of L-2 (T-3), where 1 <= p <= min{2/3 m + 5/3, m}. Notably, p is allowed to be larger than 6. (C) 2019 Elsevier Inc. All rights reserved.
引用
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页码：1087 / 1113
页数：27
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