scholarly journals Fundamental solutions for wave equation in Robertson-Walker model of universe and $L^p-L^q$ -decay estimates

2009 ◽  
Vol 2 (3) ◽  
pp. 483-502 ◽  
Author(s):  
Karen Yagdjian ◽  
◽  
Anahit Galstian
Keyword(s):  
Wave Equation ◽  
Fundamental Solutions ◽  
Decay Estimates

scholarly journals Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

2021 ◽  
Vol 54 (1) ◽  
pp. 245-258
Author(s):  
Younes Bidi ◽  
Abderrahmane Beniani ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Wave Equation ◽  
Global Solution ◽  
Fractional Laplacian ◽  
Necessary Conditions ◽  
Dynamic Structure ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Structure Of Solutions ◽  
Nonlinear Source ◽  
Galerkin Approximations

Abstract We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

scholarly journals Growth estimates in linear elasticity with a sublinear body force without definiteness conditions on the elasticities

1984 ◽  
Vol 27 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Franca Franchi
Keyword(s):  
Wave Equation ◽  
Body Force ◽  
Displacement Vector ◽  
Fundamental Solutions ◽  
Existence Results ◽  
The Body ◽  
Heat Diffusion ◽  
Initial Value ◽  
Linear Elastic ◽  
Linear Elastic Body

In this paper, we study the boundary-initial value problem for a linear elastic body ina bounded domain, when the body force depends on the displacement vector u in asublinear way.Recently, much attention has been given to nonlinear body forces not only to studythe fundamental solutions of the equations governing linear elastodynamics, see e.g.Kecs [3], but also to derive global non existence results in abstract problems with directapplications to nonlinear heat diffusion or to the nonlinear wave equation, see e.g. Ball[1], Levine and Payne [10].

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