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Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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How to analyse the stability of hyperbolic balance laws with diffusion?

Assume we have the following system of balance laws: $$ U_t+\partial_x F(U,x)=S(U,x)+\partial_x(D(U,x)U_x). $$ Is there any method to analyse the stability of its solution (assume that the solution e …
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