Email this article Existence of Weak Solutions to an Elliptic-Parabolic Equation with Variable Order of Nonlinearity
- Authors: Mukminov F.K.1, Andriyanova E.R.2,3
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Affiliations:
- Institute of Mathematics with Computer Center, Ufa Science Center of the Russian Academy of Sciences
- Australian Mathematical Sciences Institute
- Australian National University
- Issue: Vol 241, No 3 (2019)
- Pages: 290-305
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/242887
- DOI: https://doi.org/10.1007/s10958-019-04424-5
- ID: 242887
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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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