A semigroup approach to an integro-differential equation modeling slow erosion |
| |
Authors: | Alberto Bressan Wen Shen |
| |
Institution: | Department of Mathematics, Penn State University, University Park, PA 16802, USA |
| |
Abstract: | The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u=u(t,x) can have jumps, the inverse function x=x(t,u) is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme combined with a nonlinear projection operator, we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law. Going back to the original variables, this yields the global well-posedness of the Cauchy problem for the granular flow model. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|