Accurate estimates for the amplitude and support of unbounded solutions of the non-linear heat-conduction equation with a source

1990 ◽  
Vol 30 (2) ◽  
pp. 67-74
Author(s):  
V.A. Galaktionov
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Unbounded Solutions ◽  
Linear Heat ◽  
Non Linear

scholarly journals Non-linear unsteady inverse boundary problem for heat conduction equation

2017 ◽  
Vol 38 (2) ◽  
pp. 81-100 ◽  
Author(s):  
Magda Joachimiak ◽  
Michał Ciałkowski
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Linear Problem ◽  
Conduction Equation ◽  
Direct And Inverse Problems ◽  
Heat Conduction Coefficient ◽  
Nitrification Process ◽  
Non Linear ◽  
Unsteady Heat Conduction ◽  
Inverse Boundary Problem

AbstractDirect and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff’s substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.

scholarly journals Non-differentiable solutions for non-linear local fractional heat conduction equation

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 309-314
Author(s):  
Sheng Zhang ◽  
Xiaowei Zheng
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Heat Conduction Equation ◽  
Bäcklund Transformation ◽  
Conduction Equation ◽  
Reduced Form ◽  
Backlund Transformation ◽  
Fractal Structures ◽  
Non Linear ◽  
Fractional Heat Conduction

Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation of a reduced form of the local fractional heat conduction equation is constructed by Painleve analysis. Based on the Backlund transformation, some exact non-differentiable solutions of the local fractional heat conduction equation are obtained. To gain more insights of the obtained solutions, two solutions are constrained to a Cantor set and then two spatio-temporal fractal structures with profiles of these two solutions are shown. This paper further reveals by local fractional heat conduction equation that fractional calculus plays important role in dealing with non-differentiable problems.

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