Global existence of solutions to the initial-boundary value problem of conservation law with degenerate diffusion term

In this paper we explore the classical solutions to the conservation law with degenerate diffusion term (u(t) - Delta(x')u = div f (u), x epsilon Omega subset of R-n, t > 0, with x = (x(1), x')). We establish the global existence and exponential decay estimates to the solutions of the initial boundary value problem in domain Omega = R x Pi(n)(i=2)(O, L-i). Meanwhile, to clarify the viscous effect of the degenerate diffusion term, we also investigate the classical solutions to the Cauchy problem of the modified equation u(t) - Delta(x')u = (1 - chi (D)) div f (u), x epsilon R-n, t > 0, with chi (D) a Fourier multiplier operator, we use the frequency decomposition method to establish the global existence and the polynomial decay estimates. (c) 2012 Elsevier Ltd. All rights reserved.