Generalized Solution of the Riemann Problem for Some Scalar Balance Law with Singular Source Term
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)...
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| Format: | Others |
| Language: | en_US |
| Published: |
2006
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| Online Access: | http://ndltd.ncl.edu.tw/handle/p8ym5y |
| Summary: | 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.
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