scholarly journals On an exact solution to the nonlinear heat equation with a source

2021 ◽  
Vol 1847 (1) ◽  
pp. 012006
Author(s):  
A L Kazakov ◽  
A A Lempert ◽  
L F Spevak
Keyword(s):  
Exact Solution ◽  
Heat Equation ◽  
Nonlinear Heat Equation

scholarly journals A regularized method for two dimensional nonlinear heat equation backward in time

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 289-303 ◽  
Author(s):  
Huy Tuan ◽  
Duc Trong ◽  
Hoang Quan
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Nonlinear Heat Equation ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Local Boundary ◽  
Problem Method ◽  
Non Local ◽  
Regularized Method

In this paper, a non-local boundary value problem method for solving 2-D nonlinear heat equation backward in time is given. Some error estimates between the exact solution and its regularization approximation are provided and numerical examples show that the method works effectively.

scholarly journals Adomian Decomposition Method for a Nonlinear Heat Equation with Temperature Dependent Thermal Properties

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Ghulam Mohammad ◽  
M. T. Mustafa ◽  
F. D. Zaman
Keyword(s):  
Exact Solution ◽  
Heat Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Nonlinear Heat Equation ◽  
Temperature Dependent ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Method Analysis

The solutions of nonlinear heat equation with temperature dependent diffusivity are investigated using the modified Adomian decomposition method. Analysis of the method and examples are given to show that the Adomian series solution gives an excellent approximation to the exact solution. This accuracy can be increased by increasing the number of terms in the series expansion. The Adomian solutions are presented in some situations of interest.

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

scholarly journals Null controllability of a nonlinear heat equation

2002 ◽  
Vol 7 (7) ◽  
pp. 375-383 ◽  
Author(s):  
G. Aniculăesei ◽  
S. Aniţa
Keyword(s):  
Heat Equation ◽  
Dirichlet Boundary ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Nonlinear Heat Equation ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Linearized System ◽  
Kakutani Fixed Point ◽  
Exact Null Controllability ◽  
Kakutani Fixed Point Theorem

We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system. The result extends to the case of boundary control.

Lie symmetries and invariants for a 2D nonlinear heat equation

2008 ◽  
Vol 68 (8) ◽  
pp. 2261-2268 ◽  
Author(s):  
Rodica Cimpoiasu ◽  
Radu Constantinescu
Keyword(s):  
Heat Equation ◽  
Lie Symmetries ◽  
Nonlinear Heat Equation
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