We consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation (ut+uux)x=1/2ux2 with the simplest initial data such that ux blows up in finite time. We prove that the zero-viscosity limit selects a unique global weak solution of the partial differential equation without viscosity. We also present numerical experiments which indicate that the zero-dispersion limit selects a different global weak solution of the same initial-value problem.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering