Explicit calculation of strong solution on linear parabolic equation

2013/11/23 by Xiaoping Fang, Fang, Xiaoping, Youjun Deng +3
Computer Science · Mathematics · #35C20 #35K05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #math.AP #msc:35C20 #msc:35K05

paper · pdf · doi:10.48550/arxiv.1311.5970

10 pages

arxiv created 2013/11/23 · openalex publication_date 2013/11/23 · arxiv updated 2013/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give the existence and uniqueness of the strong solution of one dimensional linear parabolic equation with mixed boundary conditions. The boundary conditions can be any kind of mixed Dirichlet, Neumann and Robin boundary conditions. We use the extension method to get the unique solution. Furthermore, the method can also be easily implemented as a numerical method. Some simple examples are presented.

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