Initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition

2014/12/16 by Alexander Gladkov, Gladkov, Alexander, Tatiana Kavitova +1
Mathematics · #35K20 #35K58 #35K61 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1412.5021

openalex publication_date 2014/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Related

• Initial boundary value problem for a semilinear parabolic equation with\n absorption and nonlinear nonlocal boundary condition
• Local existence of solutions and comparison principle for initial boundary value problem with nonlocal boundary condition for a nonlinear parabolic equation with memory
• Global existence and blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition
• Blow-up problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition
• Global existence of classical solutions for a nonlocal one dimensional parabolic free boundary problem