scholarly journals Random attractors for stochastic time-dependent damped wave equation with critical exponents

2020 ◽  
Vol 25 (7) ◽  
pp. 2793-2824
Author(s):  
Qingquan Chang ◽  
◽  
Dandan Li ◽  
Chunyou Sun
Keyword(s):  
Wave Equation ◽  
Critical Exponents ◽  
Time Dependent ◽  
Damped Wave Equation ◽  
Random Attractors ◽  
Stochastic Time

BLOW-UP OF THE SOLUTION FOR SEMILINEAR DAMPED WAVE EQUATION WITH TIME-DEPENDENT DAMPING

2012 ◽  
Vol 14 (05) ◽  
pp. 1250034
Author(s):  
JIAYUN LIN ◽  
JIAN ZHAI
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Initial Data ◽  
Upper Bound ◽  
Blow Up ◽  
Time Dependent ◽  
Damped Wave Equation ◽  
Large Initial Data ◽  
Power Type ◽  
The Cauchy Problem

We consider the Cauchy problem for the damped wave equation with time-dependent damping and a power-type nonlinearity |u|ρ. For some large initial data, we will show that the solution to the damped wave equation will blow up within a finite time. Moreover, we can show the upper bound of the life-span of the solution.

scholarly journals Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

2021 ◽  
Author(s):  
Jakub Banaśkiewicz ◽  
Piotr Kalita
Keyword(s):  
Wave Equation ◽  
Galerkin Method ◽  
Growth Condition ◽  
Global Attractor ◽  
Time Dependent ◽  
Strichartz Estimates ◽  
Damped Wave Equation ◽  
Independent Function ◽  
The Galerkin Method

AbstractWe study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah–Struwe solutions, which satisfy the Strichartz estimates and coincide with the class of solutions obtained by the Galerkin method. For this class we show the existence and smoothness of pullback, uniform, and cocycle attractors and the relations between them. We also prove that these non-autonomous attractors converge upper-semicontinuously to the global attractor for the limit autonomous problem if the time-dependent nonlinearity tends to a time independent function in an appropriate way.

scholarly journals Decay result in a problem of a nonlinearly damped wave equation with variable exponent

2021 ◽  
Vol 7 (2) ◽  
pp. 3067-3082
Author(s):  
Mohammad Kafini ◽  
◽  
Jamilu Hashim Hassan ◽  
Mohammad M. Al-Gharabli ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Galerkin Approximation ◽  
Stability Result ◽  
Time Dependent ◽  
Damped Wave Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Frictional Damping

<abstract><p>In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.</p></abstract>

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.

An exact non reflecting boundary condition for 2D time-dependent wave equation problems

Wave Motion ◽  
2014 ◽  
Vol 51 (1) ◽  
pp. 168-192 ◽  
Author(s):  
Silvia Falletta ◽  
Giovanni Monegato
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Time Dependent
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