On a comparison theorem for parabolic equations with nonlinear boundary conditions-Reference-Cited by-同舟云学术

On a comparison theorem for parabolic equations with nonlinear boundary conditions

Published:2022-01-01 Issue:1 Volume:11 Page:1165-1181
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Kita Kosuke¹,Ôtani Mitsuharu²

Affiliation:

1. Graduate School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku , Tokyo , 169-8555 , Japan

2. Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku , Tokyo , 169-8555 , Japan

Abstract

Abstract In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary condition. The advantage of our comparison theorem over the classical ones lies in the fact that it enables us to compare two solutions satisfying different types of boundary conditions. As an application of our comparison theorem, we can give some new results on the existence of blow-up solutions of some parabolic equations and systems with nonlinear boundary conditions.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2022-0239/pdf

Reference14 articles.

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5. H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, In: Contributions to Nonlinear Functional Analysis, E. Zarantonelloeditor, Academic Press, Madison, 1971, pp. 101–156.

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