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Seminar on nonlinear problems of partial differential equations and mathematical physics
September 21, 2021 18:00–19:30, Moscow
 


On the critical exponent "instantaneous blow-up / local solvability" in the Cauchy problem for a model Sobolev type equation.

A. A. Panin, M. O. Korpusov

Faculty of Physics, Lomonosov Moscow State University

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Abstract: A Sobolev type equation with non-isotropic spatial operator and power gradient nonlinearity is considered. It is shown, by means of the nonlinear capacity method, that for the powers 1<𝑞≤3/2 there is no weak solution to the Cauchy problem for a wide class of initial data. However, for q>3/2 a local weak solution exists, as the the constraint mapping method with Green's function shows.

Website: https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%2266c4b047-af30-41c8-9097-2039bac83cbc%22%7d

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