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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.
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참고문헌 (15)
참고문헌 신청
A. B. Aliev / 2010 / Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations / Nonlinear Anal 72 (7-8) :
A. B. Aliev / 2012 / Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping te
B. Said-Houari / 2010 / Global nonexistence of positive initial-energy solutions of a system of nonlinear wave equations with damping and source terms / Differential Integra
B. X. Wang / 2004 / Nonlinear scattering theory for a class of wave equations in Hs / J. Math. Anal. Appl 296 (1) : 74 ~ 96
C. X. Miao / 1995 / Time-space estimates and scattering at low energy for higher-order wave equations / Acta Math. Sinica 38 (5) : 708 ~ 717
A. B. Aliev / 2012 / Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping te
B. Said-Houari / 2010 / Global nonexistence of positive initial-energy solutions of a system of nonlinear wave equations with damping and source terms / Differential Integra
B. X. Wang / 2004 / Nonlinear scattering theory for a class of wave equations in Hs / J. Math. Anal. Appl 296 (1) : 74 ~ 96
C. X. Miao / 1995 / Time-space estimates and scattering at low energy for higher-order wave equations / Acta Math. Sinica 38 (5) : 708 ~ 717
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