Premium
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.