Reduction of Certain Type of Parabolic Partial Differential Equations to Heat Equation

AUTHOR AND
AFFILIATION

DHRUTI B. JOSHI
Lecturer in Mathematics, Government Polytechnic, Himmatnagar – 383001 (India)
A. K. DESAI
Former Head of The Department of Mathematics, School of Sciences, Gujarat University Ahmedabad – 380009 (India)

KEYWORDS:

Parabolic Partial Differential Equation, Heat Equation, Solution of First Order Linear PDE, AMS Subject Classification(2010): 35K05; 35K10; 35F05; 35A25

Issue Date:

September 2018

Pages:

353-361

ISSN:

2319-8044 (Online) – 2231-346X (Print)

Source:

Vol.30 – No.9

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DOI:

http://dx.doi.org/10.22147/jusps-A/300901

ABSTRACT:

As we all know that the solution of Heat Equation is found more easily than other Partial Differential Equations of Parabolic Type. So, if we enable us to convert Parabolic Partial Differential Equations to Heat Equation, then it becomes easier to find solutions. In this paper we are considering a method introduced by Harper and with the help of a method for reduction of some types of Partial Differential Equations to their Canonical Form it is shown that all the equations of this type are reduced to Heat Equation by following some definite steps. To illustrate the method, we have taken some PDEs of this type and converted them to their Canonical Form and then to Heat Equation.

Copy the following to cite this Article:

D. B. Joshi; A. K. Desai, “Reduction of Certain Type of Parabolic Partial Differential Equations to Heat Equation”, Journal of Ultra Scientist of Physical Sciences, Volume 30, Issue 9, Page Number 353-361, 2018


Copy the following to cite this URL:

D. B. Joshi; A. K. Desai, “Reduction of Certain Type of Parabolic Partial Differential Equations to Heat Equation”, Journal of Ultra Scientist of Physical Sciences, Volume 30, Issue 9, Page Number 353-361, 2018

Available from: http://www.ultrascientist.org/paper/1491/reduction-of-certain-type-of-parabolic-partial-differential-equations-to-heat-equation


As we all know that the solution of Heat Equation is found more easily than other Partial Differential Equations of Parabolic Type. So, if we enable us to convert Parabolic Partial Differential Equations to Heat Equation, then it becomes easier to find solutions. In this paper we are considering a method introduced by Harper and with the help of a method for reduction of some types of Partial Differential Equations to their Canonical Form it is shown that all the equations of this type are reduced to Heat Equation by following some definite steps. To illustrate the method, we have taken some PDEs of this type and converted them to their Canonical Form and then to Heat Equation.