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Category: Issue 9

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

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)

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.

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


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...

Fixed Point Theorems and its Applications in Partial and Generalized Partial Cone Metric Spaces

VARSHA SHRIVASTAVA
H.No. 100, Gomti colony, Nehru Nagar, Bhopal (India)
RIZWANA JAMAL
Professor, Department of Mathematics, Safia Science College, Bhopal (India)
ANIL RAJPUT
Professor and HOD, Department of Mathematics, Chandra Shekhar Azad Govt. P.G. College, Sehore (India)

ABSTRACT:

The main purpose of this paper is to prove some fixed point theorems and its applications in partial and generalized partial cone metric spaces. Our results are satisfying various contractive conditions on cone spaces. We also prove the uniqueness of such fixed points theorems

KEYWORDS: Fixed Point Theorems, Partial Cone Metric Spaces


The main purpose of this paper is to prove some fixed point theorems and its applications in partial and generalized partial cone metric spaces. Our results are satisfying various...

Fixed Point Theorems for Set Valued Contraction Integral Type in Complete Metric Space

NEELAM WASNIK
Department of Mathematics, Govt. Girls College, Sehore (India)
ANIL RAJPUT
Department of Mathematics, CSA Govt. P.G. College, Sehore, M.P. (India)

ABSTRACT:

In this paper, we shall establish some stability results for Picard and Mann iteration processes in metric space and normed linear space by employing a set-valued contractive condition of integral type

KEYWORDS: Contraction Integral Type, Fixed Point Theorems


In this paper, we shall establish some stability results for Picard and Mann iteration processes in metric space and normed linear space by employing a set-valued contractive condition of...