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Scientific seminar on the differential and functional differential equations
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The Cauchy–Gelfand problem and the inverse problem for a first-order quasilinear equation A. A. Shananinab, G. M. Henkin a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region b Nikol'skii Mathematical Institute of Peoples' Friendship University of Russia, Moscow |
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Abstract: We consider the problem posed by Gelfand on the asymptotics in time of the solution of the Cauchy problem for a first-order quasilinear equation with Riemann-type initial conditions. Based on the method of vanishing viscosity with uniform estimates, exact asymptotics in the Cauchy-Gelfand problem are obtained without a priori assumption of monotonicity of the initial data. The initial data parameters responsible for the localization of shock waves are described. |
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