Abstract
A general idea for solving hyperbolic systems of conservation laws is to use a local relaxation approximation. The motivation is to have a simple discrete velocity kinetic type relaxation regularization which approximates the original system with a small dissipative correction. In this paper we extend the previous approach to systems of nonlinear parabolic equations. The corresponding relaxation schemes are also constructed. The new approximation, while maintaining the advantages of that constructed for systems of conservation laws, at the cost of one more rate equation permits to transform second order nonlinear systems to semi-linear first order ones.
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Naldi, G., Pareschi, L., Toscani, G. (1999). Hyperbolic Relaxation Approximation to Nonlinear Parabolic Problems. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_25
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_25
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