This talk will be focused on the non-classical solutions to some hyperbolic systems of conservation laws and scalar conservation laws with discontinuous flux. We use the method of vanishing pressure limit and vanishing viscosity limit to construct solutions. For scalar conservation laws with discontinuous flux, we propose a generalized weak solution based on the vanishing viscosity limit. We then introduce a numerical scheme for this scalar conservation law that effectively captures the solution and we also do its convergence analysis. Next, we establish a Hopf-Lax type formula for the solution to the initial-boundary value problem for the 1D pressureless gas dynamics model by introducing generalized potentials.
SMS Conference Room
Mr. Abhrojyoti Sen.
Solutions in the class of measures for some hyperbolic systems of conservation laws and scalar conservation laws with discontinuous flux.