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References (31)
-
F. Merle, H. Zaag (2008)
Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave EquationCommunications in Mathematical Physics, 282
-
(1998)
Remarks on blowup of solutions for nonlinear evolution equations of second order -
F Gazzola, M Squassina (2006)
Global solutions and finite time blow up for damped semilinear wave equationsAnn. I. H. Poincaré AN, 23
-
Wenying Chen, Yong Zhou (2009)
Global nonexistence for a semilinear Petrovsky equationNonlinear Analysis-theory Methods & Applications, 70
-
Z. Nehari (1960)
On a class of nonlinear second-order differential equationsTransactions of the American Mathematical Society, 95
-
V. Georgiev, G. Todorova (1994)
Existence of a Solution of the Wave Equation with Nonlinear Damping and Source TermsJournal of Differential Equations, 109
-
A. Carvalho, J. Cholewa (2002)
Local well posedness for strongly damped wave equations with critical nonlinearitiesBulletin of the Australian Mathematical Society, 66
-
H. Levine, G. Todorova, G. Todorova (2000)
Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy, 129
-
A. Boukricha (2004)
Nonlinear Semigroups -
F. Gazzola, M. Squassina (2006)
Global solutions and finite time blow up for damped semilinear wave equations ? ? The first author wAnnales De L Institut Henri Poincare-analyse Non Lineaire
-
D. SAIqOER (2004)
On Global Solution of Nonlinear Hyperbolic Equations -
Yong Zhou (2005)
Global existence and nonexistence for a nonlinear wave equation with damping and source termsMath. Nachr., 278
-
MR Li, LY Tsai (2003)
Existence and nonexistence of global solution of some system of semilinear wave equationsNonlinear Anal., 54
-
Yong Zhou (2005)
A blow-up result for a nonlinear wave equation with damping and vanishing initial energy in (M, d)Appl. Math. Lett., 18
-
Fuqin Sun, Mingxin Wang (2006)
Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms☆Nonlinear Analysis-theory Methods & Applications, 64
-
A. Ambrosetti, P. Rabinowitz (1973)
Dual variational methods in critical point theory and applicationsJournal of Functional Analysis, 14
-
T. Cazenave (1985)
Uniform estimates for solutions of nonlinear Klein-Gordon equationsJournal of Functional Analysis, 60
-
H. Levine (1974)
Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave EquationsSiam Journal on Mathematical Analysis, 5
-
(1975)
Nonhomogeneous Boundary Value Problems, vol -
F. Merle, H. Zaag (2007)
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimensionJournal of Functional Analysis, 253
-
R. Ikehata, Takashi Suzuki (1996)
Stable and unstable sets for evolution equations of parabolic and hyperbolic typeHiroshima Mathematical Journal, 26
-
M. Nakao, K. Ono (1993)
Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equationsMathematische Zeitschrift, 214
-
(1996)
Minimax Theorems, Progress Nonlinear Differential Equations Applications, vol -
F. Gazzola (2004)
Finite-time blow-up and global solutions for some nonlinear parabolic equationsDifferential and Integral Equations
-
H. Levine, J. Serrin (1997)
Global Nonexistence Theorems for Quasilinear Evolution Equations with DissipationArchive for Rational Mechanics and Analysis, 137
-
J. Esquivel-Avila (2003)
The dynamics of a nonlinear wave equationJournal of Mathematical Analysis and Applications, 279
-
Enzo Vitillaro (1999)
Global Nonexistence Theorems for a Class of Evolution Equations with DissipationArchive for Rational Mechanics and Analysis, 149
-
K. Nishihara (1997)
Asymptotic Behavior of Solutions of Quasilinear Hyperbolic Equations with Linear DampingJournal of Differential Equations, 137
-
F. Merle, H. Zaag (2005)
Determination of the blow-up rate for a critical semilinear wave equationMathematische Annalen, 331
-
J. Esquivel-Avila (2004)
QUALITATIVE ANALYSIS OF A NONLINEAR WAVE EQUATIONDiscrete and Continuous Dynamical Systems, 10
-
P. Pucci, J. Serrin (1998)
Global Nonexistence for Abstract Evolution Equations with Positive Initial EnergyJournal of Differential Equations, 150
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-016-0339-x
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, an initial boundary value problem for a system of semi-linear hyperbolic equations with damped term in a bounded domain is considered. We prove the global existence, uniquenes, blow up of solutions and give some estimates for the lifespan of solutions.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Apr 9, 2016