Initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition
Alexander Gladkov, Tatiana Kavitova
TL;DR
This paper investigates an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary conditions, establishing comparison principles, local existence, and conditions for uniqueness and nonuniqueness.
Contribution
It introduces new theoretical results on existence, uniqueness, and nonuniqueness for solutions of semilinear parabolic equations with complex boundary conditions.
Findings
Established comparison principle for the problem
Proved local existence of solutions
Identified conditions leading to nonuniqueness
Abstract
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of uniqueness and nonuniqueness
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Numerical methods in inverse problems