Global existence and optimal decay rates of solutions to conservation laws with diffusion‐type terms |
| |
Authors: | Lijuan Wang |
| |
Institution: | School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, China |
| |
Abstract: | We consider the Cauchy problem on nonlinear scalar conservation laws with a diffusion‐type source term. Based on a low‐frequency and high‐frequency decomposition, Green's function method and the classical energy method, we not only obtain L2 time‐decay estimates but also establish the global existence of solutions to Cauchy problem when the initial data u0(x) satisfies the smallness condition on , but not on . Furthermore, by taking a time‐frequency decomposition, we obtain the optimal decay estimates of solutions. Copyright © 2016 John Wiley & Sons, Ltd. |
| |
Keywords: | conservation laws diffusion‐type term Green function time‐frequency decomposition optimal time‐decay estimates |
|
|