Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping terms

2012 ◽  
Vol 75 (1) ◽  
pp. 91-102 ◽  
Author(s):  
Akbar B. Aliev ◽  
Anar A. Kazimov
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Hyperbolic Equations ◽  
Global Solutions ◽  
The Cauchy Problem

scholarly journals GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CAUCHY PROBLEM OF A DISSIPATIVE BOUSSINESQ-TYPE EQUATION

2017 ◽  
Vol 22 (4) ◽  
pp. 441-463 ◽  
Author(s):  
Amin Esfahani ◽  
Hamideh B. Mohammadi
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Contraction Mapping ◽  
Type Equation ◽  
Global Solutions ◽  
Contraction Mapping Principle ◽  
Equation Modeling ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
The Cauchy Problem

We consider the Cauchy problem for a Boussinesq-type equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle.

scholarly journals Generalized quasilinear hyperbolic equations and Yosida approximations

2003 ◽  
Vol 74 (1) ◽  
pp. 69-86 ◽  
Author(s):  
Jong Yeoul Park ◽  
Il Hyo Jung ◽  
Yong Han Kang
Keyword(s):  
Cauchy Problem ◽  
Boundary Conditions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Hyperbolic Equations ◽  
Global Solutions ◽  
Global Solvability ◽  
Nonlinear Evolution Equations ◽  
Damping Term ◽  
The Cauchy Problem

AbstractWe will show the existence, uniqueness and regularity of global solutions for the Cauchy problem for nonlinear evolution equations with the damping term .As an application of our results, we give the global solvability and regularity of the mixed problem with Dirichiet boundary conditions:

scholarly journals Symmetries and solutions to dissipative hyperbolic geometric flow

2021 ◽  
Author(s):  
Fang Gao ◽  
Zenggui Wang
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Riemann Surfaces ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Global Solutions ◽  
Geometric Flows ◽  
Geometric Flow ◽  
The Cauchy Problem ◽  
Symmetric Method

Based on the Lie-symmetric method, we study the solutions of dissipative hyperbolic geometric flows on Riemann surfaces; In the process of simplification, the mixed equations are produced. And the hyperbolic equations are obtained under limited conditions. Considering the Cauchy problem of the hyperbolic equation, the existence and uniqueness conditions of the global solutions are obtained. Finally, the phenomenon of blow up is discussed.

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