Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations

2010 ◽  
Vol 72 (7-8) ◽  
pp. 3275-3288 ◽  
Author(s):  
Akbar B. Aliev ◽  
Bijan H. Lichaei
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Global Solutions ◽  
Higher Order ◽  
The Cauchy Problem

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.

scholarly journals The Cauchy Problem for Higher-Order KP Equations

1999 ◽  
Vol 153 (1) ◽  
pp. 196-222 ◽  
Author(s):  
J.C. Saut ◽  
N. Tzvetkov
Keyword(s):  
Cauchy Problem ◽  
Higher Order ◽  
The Cauchy Problem ◽  
Kp Equations
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