Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion
We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form u_t + f(u)_x = ε u_xx − δ(|u_xx|^n)_x. Convergence of the solutions {u^(ε,δ)} to the entropy weak solution of the hyperbolic limit equation u_t + f(u)_x = 0, for all re...
| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2020
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10174/26655 |
| Country: | Portugal |
| Oai: | oai:dspace.uevora.pt:10174/26655 |
| Summary: | We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form u_t + f(u)_x = ε u_xx − δ(|u_xx|^n)_x. Convergence of the solutions {u^(ε,δ)} to the entropy weak solution of the hyperbolic limit equation u_t + f(u)_x = 0, for all real numbers 1 ≤ n ≤ 2 is proved if δ = o(ε^(3n−1)/2 ; ε^(5n−1)/2(2n−1) ). |
|---|