scholarly journals On the summability of the solutions of the inhomogeneous heat equation with a power-law nonlinearity and variable coefficients

2021 ◽  
Vol 494 (2) ◽  
pp. 124656
Author(s):  
Pascal Remy
Keyword(s):  
Heat Equation ◽  
Power Law ◽  
Variable Coefficients

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

scholarly journals Borel summability of the heat equation with variable coefficients

2012 ◽  
Vol 252 (4) ◽  
pp. 3076-3092 ◽  
Author(s):  
O. Costin ◽  
H. Park ◽  
Y. Takei
Keyword(s):  
Heat Equation ◽  
Variable Coefficients ◽  
Borel Summability

On Standard Eigenvalues of Variable-Coefficient Heat and Rod Equations

1989 ◽  
Vol 56 (1) ◽  
pp. 146-148 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Heat Equation ◽  
Power Law ◽  
Heat Conductivity ◽  
Variable Coefficient ◽  
Continuous Case ◽  
Coefficient Function ◽  
Heat Conductivity Coefficient ◽  
One Dimensional ◽  
Variable Heat ◽  
The One

Forms of the variable-heat-conductivity coefficient function in the one-dimensional heat equation are determined which yield a standard harmonic eigenvalue sequence as in the case of homogeneity. The continuous case is found to correspond to a four-thirds power law dependence on coordinate. For the stepped case, the condition on the ratio of segmental heat conductivities in terms of the junction location is presented.

Sign in / Sign up

Export Citation Format

Share Document