On the decay of solutions for a class of quasilinear hyperbolic equations with non‐linear damping and source terms | Zendy

Messaoudi Salim A. | Zendy

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On the decay of solutions for a class of quasilinear hyperbolic equations with non‐linear damping and source terms

Author(s) -

Messaoudi Salim A.

Publication year - 2005

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.641

Subject(s) - mathematics , dirichlet boundary condition , class (philosophy) , wave equation , exponential decay , mathematical analysis , work (physics) , exponential function , boundary value problem , dirichlet distribution , physics , thermodynamics , quantum mechanics , artificial intelligence , computer science

In this paper, we consider the non‐linear wave equation$$u_{tt}-\Delta u_{t}-{\rm{div}} (| \nabla u|^{m}\nabla u) +a|u_{t}|^{\alpha}u_{t}=b|u|^{p}u$$a , b >0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on α , m , and p , we give precise decay rates for the solution. In particular, we show that for m =0, the decay is exponential. This work improves the result by Yang ( Math. Meth. Appl. Sci. 2002; 25 :795–814). Copyright © 2005 John Wiley & Sons, Ltd.

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