Non-classical shock waves to the perturbed Riemann problem of two-by-two resonant balance law

• Main Authors: Kou-Feng Tang, 唐國峰
• Other Authors: Tzi-Sheng Yang
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/75740429831286630279

碩士 === 東海大學 === 數學系 === 98 === We give a new approach of constructing the generalized entropy solution to the Riemann problem of scalar nonlinear balance law with singular source term. The source term is singular in the sense that it is a product of delta function and a discontinuous function, which is undefined in the distribution sense. By perturbing the singular source term with a smooth one, we study the perturbed Riemann problem. We prove that if the perturbed source term is monotonic and convex, then the solution of the perturbed Riemann problem is stable. In this case we established the generalized entropy solution of Riemann problem, which is the limit of the solution to perturbed Riemann problem. Due the resonance of the system, there exists non-classical weak solution in which entropy condition does not satisfy, but still self-similar. Thus, the Lax's method can be extended to resonant scalar nonlinear balance law with singular source term.