具变指数源项和强阻尼项的波动方程解的渐近稳定性

Abstract

Abstract:

This paper deals with the following wave equation with strong damping term:

$u_{tt}-{\rm div}(|\nabla{u}|^{p(x)-2}\nabla{u})-\Delta u_t=|u|^{q(x)-2}u$

under initial and Dirichlet boundary value condition. By constructing a new control function and applying the Sobolev embedding inequality, the authors establish the relationship between source term and energy functional, and then decay estimates are obtained by means of Komornik's inequality and energy estimates. At last, we prove that u(x, t)=0 is asymptotic stable.

Key words: Damping term, Decay estimates, Asymptotic stability

CLC Number:

Menglan Liao,Bin Guo. Asymptotic Stability of Weak Solutions to Wave Equation with Variable Exponents and Strong Damping Term[J].Acta mathematica scientia,Series A, 2020, 40(1): 146-155.

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References 16

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Asymptotic Stability of Weak Solutions to Wave Equation with Variable Exponents and Strong Damping Term

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