Open AccessOn the maximum principle for a class of nonlinear parabolicequations
Author(s) -
A. A. Kon’kov
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-89-92
Subject(s) - nonlinear system , class (philosophy) , mathematics , maximum principle , tikhonov regularization , mathematical analysis , space (punctuation) , order (exchange) , type (biology) , mathematical optimization , computer science , physics , inverse problem , economics , optimal control , ecology , finance , quantum mechanics , artificial intelligence , biology , operating system
In this paper, we consider solutions of nonlinear parabolic equations in the half-space.It is well-known that, in the case of linear equations, one needs to impose additional conditions on solutions for the validity of the maximum principle. The most famous of them are the conditions of Tikhonov and T¨acklind. We show that such restrictions are not needed for a wide class of nonlinear equations. In so doing, the coecients of lower-order derivatives can grow arbitrarily as the spatial variables tend to innity.We give an example which demonstrates an application of the obtained re- sults for nonlinearities of the Emden - Fowler type.