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 (ut−Δx′u=divf(u),x∈Ω⊂Rn,t>0, with x=(x1,x′)x=(x1,x′)). We establish the global existence and exponential decay estimates to the solutions of the initial boundary value problem in domain Ω=R×∏i=2n(0,Li). 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 ut−Δx′u=(1−χ(D))divf(u),x∈Rn,t>0, with χ(D)χ(D) a Fourier multiplier operator, we use the frequency decomposition method to establish the global existence and the polynomial decay estimates.