A constructive theory for shock-free,isentropic flow |
| |
Authors: | David Hoff |
| |
Institution: | Department of Mathematics, Indiana University, Bloomington, Indiana 47405 U.S.A. |
| |
Abstract: | We construct by finite differences solutions of the Cauchy problem for the nonlinear wave equation in one space dimension. We make certain monotonicity assumptions about the initial data, and we show that the resulting solution is Lipschitz continuous for positive times. In addition, we prove the uniqueness of the solution in a certain class, and we characterize its large-time behavior in terms of the equilibrium state for a corresponding Riemann problem. Finally, we show how our results can be extended to more general 2 × 2 systems of hyperbolic conservation laws which are genuinely nonlinear. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|