Abstract
We give a new approach of constructing the generalized entropy solutions to the Riemann problem of scalar nonlinear balance laws with singular source terms. The source term is singular in the sense that it is a product of delta function and a discontinuous function, which is undefined in distribution. By re-formulating the source term, we study the corresponding perturbed Riemann problem. The existence and stability of perturbed Riemann solutions is established under some entropy condition so that the generalized entropy solutions of Riemann problem can be interpreted as the limit of corresponding perturbed Riemann solutions. The self-similarity of generalized entropy solutions is also obtained, which means that Lax's method in [13] can be extended to scalar nonlinear balance laws with singular source terms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have