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

页码：1087 / 1113

页数：27

共 27 条

[11] Global solutions and finite time blow up for damped semilinear wave equations [J].

Gazzola, F ;

Squassina, M .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (02) :185-207

[12] EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS [J].

GEORGIEV, V ;

TODOROVA, G .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 109 (02) :295-308

[13]

Grafakos L, 2008, GRAD TEXTS MATH, V249, P1, DOI 10.1007/978-0-387-09432-8_1

[14] Energy decay of a viscoelastic wave equation with supercritical nonlinearities [J].

Guo, Yanqiu ;

Rammaha, Mohammad A. ;

Sakuntasathien, Sawanya .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2018, 69 (03)

[15] Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities [J].

Guo, Yanqiu ;

Rammaha, Mohammad A. ;

Sakuntasathien, Sawanya .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (03) :1956-1979

[16] Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping [J].

Guo, Yanqiu ;

Rammaha, Mohammad A. ;

Sakuntasathien, Sawanya ;

Titi, Edriss S. ;

Toundykov, Daniel .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (10) :3778-3812

[17]

Guo YQ, 2013, BULL INST MATH ACAD, V8, P445

[18] SYSTEMS OF NONLINEAR WAVE EQUATIONS WITH DAMPING AND SUPERCRITICAL BOUNDARY AND INTERIOR SOURCES [J].

Guo, Yanqiu ;

Rammaha, Mohammad A. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (05) :2265-2325

[19] Blow-up of solutions to systems of nonlinear wave equations with supercritical sources [J].

Guo, Yanqiu ;

Rammaha, Mohammad A. .

APPLICABLE ANALYSIS, 2013, 92 (06) :1101-1115

[20] Global existence and decay of energy to systems of wave equations with damping and supercritical sources [J].

Guo, Yanqiu ;

Rammaha, Mohammad A. .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2013, 64 (03) :621-658

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