Boundary value problems for heat equation with certain potentials in Lipschitz cylinders

2014 ◽  
Vol 26 (2) ◽  
Author(s):  
Lin Tang
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Neumann Problems ◽  
Lipschitz Cylinders

AbstractThe Dirichlet and Neumann problems of heat equation with certain potentials of the form

scholarly journals The profile near quenching time for the solution of a singular semilinear heat equation

1997 ◽  
Vol 40 (3) ◽  
pp. 437-456 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Bei Hu
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Quenching Rate ◽  
Semilinear Heat Equation ◽  
Self Similar ◽  
Initial Boundary Value ◽  
Quenching Time

We study the profile near quenching time for the solutions of the first and second initial boundary value problems (IBVP) for a semilinear heat equation. Under certain conditions, one-point quenching occurs for both first and second IBVPs. Furthermore, we derive the asymptotic self-similar quenching rate for both problems.

Uniqueness and non-uniqueness of solutions of the boundary value problems of the heat equation

2015 ◽  
Author(s):  
Meiramkul M. Amangaliyeva ◽  
Muvasharkhan T. Jenaliyev ◽  
Minzilya T. Kosmakova ◽  
Murat I. Ramazanov
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Uniqueness Of Solutions

scholarly journals Two Stage Implicit Method on Hexagonal Grids for Approximating the First Derivatives of the Solution to the Heat Equation

2021 ◽  
Vol 5 (1) ◽  
pp. 19
Author(s):  
Suzan Cival Buranay ◽  
Ahmed Hersi Matan ◽  
Nouman Arshad
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Implicit Method ◽  
Two Stage ◽  
Unconditionally Stable ◽  
Spatial Variables ◽  
Hexagonal Grids ◽  
Derivatives Of ◽  
Special Difference

The first type of boundary value problem for the heat equation on a rectangle is considered. We propose a two stage implicit method for the approximation of the first order derivatives of the solution with respect to the spatial variables. To approximate the solution at the first stage, the unconditionally stable two layer implicit method on hexagonal grids given by Buranay and Arshad in 2020 is used which converges with Oh2+τ2 of accuracy on the grids. Here, h and 32h are the step sizes in space variables x1 and x2, respectively and τ is the step size in time. At the second stage, we propose special difference boundary value problems on hexagonal grids for the approximation of first derivatives with respect to spatial variables of which the boundary conditions are defined by using the obtained solution from the first stage. It is proved that the given schemes in the difference problems are unconditionally stable. Further, for r=ωτh2≤37, uniform convergence of the solution of the constructed special difference boundary value problems to the corresponding exact derivatives on hexagonal grids with order Oh2+τ2 is shown. Finally, the method is applied on a test problem and the numerical results are presented through tables and figures.

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