Article ID Journal Published Year Pages File Type
5774534 Journal of Mathematical Analysis and Applications 2017 23 Pages PDF
Abstract
In this paper, we study the Cauchy problem for the hyperbolic p-system with time-gradually-degenerate damping term −1(1+t)λu for 0⩽λ<1, and show that the damped p-system has a couple of global solutions uniquely, and such solutions tend time-asymptotically to the shifted nonlinear diffusion waves, which are the solutions of the corresponding nonlinear parabolic equation governed by the Darcy's law. We further derive the convergence rates when the initial perturbations are in L2. The approach adopted is the technical time-weighted energy method.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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