Existence of Weak Solutions to an Elliptic-Parabolic Equation with Variable Order of Nonlinearity


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Abstract

We consider an equation with variable nonlinearity of the form |u|p(x), in which the parabolic term can vanish, i.e., in the corresponding domain the parabolic equation becomes “elliptic.” Under the weak monotonicity conditions (nonstrict inequality) we prove the existence of a solution to the first mixed problem in a cylinder with a bounded base.

About the authors

F. Kh. Mukminov

Institute of Mathematics with Computer Center, Ufa Science Center of the Russian Academy of Sciences

Author for correspondence.
Email: mfkh@rambler.ru
Russian Federation, Ufa

E. R. Andriyanova

Australian Mathematical Sciences Institute; Australian National University

Email: mfkh@rambler.ru
Australia, Melbourne; Melbourne

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