scholarly journals Local existence of $C^\infty$-solution for the initial-boundary value problem of fully nonlinear wave equation

1984 ◽  
Vol 60 (5) ◽  
pp. 149-152
Author(s):  
Yoshihiro Shibata ◽  
Yoshio Tsutsumi
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Boundary Value ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fully Nonlinear ◽  
Initial Boundary Value

scholarly journals Blowup of solutions of a nonlinear wave equation

2002 ◽  
Vol 2 (2) ◽  
pp. 105-108 ◽  
Author(s):  
Abbes Benaissa ◽  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Blowup Of Solutions ◽  
Initial Boundary Value ◽  
Blowup Result

We establish a blowup result to an initial boundary value problem for the nonlinear wave equationutt−M(‖B1/2u‖ 2) Bu+kut=|u| p−2,x∈Ω,t>0.

Asymptotic Behavior of Global Solutions for some Nonlinear Wave Equation

2014 ◽  
Vol 638-640 ◽  
pp. 1691-1694
Author(s):  
Yong Xian Yan
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Boundary Value Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Damping Term ◽  
Initial Boundary Value

In this paper we study the asymptotic behavior of the global solutions to the initial-boundary value problem of the nonlinear wave equation with damping term by applying a difference inequality.

scholarly journals Application of Initial Boundary Value Problem on Logarithmic Wave Equation in Dynamics

2018 ◽  
Author(s):  
Shkelqim Hajrulla ◽  
Leonard Bezati ◽  
Fatmir Hoxha
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Sobolev Inequality ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Initial Boundary Value ◽  
The Galerkin Method

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

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