Conditional Symmetry of Equations of Nonstationary Filtration and of the Nonlinear Heat Equation

1997 ◽  
Vol 4 (1-2) ◽  
pp. 137-140
Author(s):  
Alla Vorobyova
Keyword(s):  
Heat Equation ◽  
Nonlinear Heat Equation ◽  
Conditional Symmetry ◽  
Nonstationary Filtration

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

scholarly journals On exact solutions of the nonlinear heat equation

2019 ◽  
Vol 5 ◽  
pp. 11-17
Author(s):  
A.F. Barannyk ◽  
◽  
T.A. Barannyk ◽  
I.I. Yuryk ◽  
◽  
...  
Keyword(s):  
Heat Equation ◽  
Exact Solutions ◽  
Nonlinear Heat Equation
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