Generalized Solution of the Riemann Problem for Some Scalar Balance Law with Singular Source Term

• Main Authors: Han-Jhen Huang, 黃寒楨
• Other Authors: J.M. Hong
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/p8ym5y

碩士 === 國立中央大學 === 數學研究所 === 94 === We study the existence of generalized solutions to the Riemann problem for some scalar nonlinear balance law. The source term of equation is singular in the sense of a product of delta function and discontinuous function (so that it is undefined in distribution). We construct the generalized solutions based on a limiting process of measurable solutions (so-called perturbed Riemann solutions) for associated perturbed Riemann problem. The characteristic method is applied to study the behavior of perturbed Riemann solutions. Furthermore, the self-similarity of generalized solutions to our Riemann problem can be obtained from the limiting behavior of perturbed Riemann solutions, and this enables us to apply Lax's method to nonlinear balance laws.