Moderate dispersion in scalar conservation laws
نویسندگان
چکیده
We consider the weakly dissipative and weakly dispersive Burgers-Hopf-Korteweg-de-Vries equation with the diffusion coefficient ε and the dispersion rate δ in the range δ/ε → 0. We study the travelling wave connecting u(−∞) = 1 to u(+∞) = 0 and show that it converges strongly to the entropic shock profile as ε, δ → 0. Key-words Travelling waves, moderate dispersion, Korteweg de Vries equation, entropy solutions, dissipative-dispersive scalar conservation laws. AMS Class. No. 35B25, 35Q53, 35L67
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