Jñānābha‎, Vol. 50 (2) (2020), (38-43)

HYERS - ULAM STABILITY OF FIRST AND SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

 

By

V. P. Sonalkar 1,  A. N. Mohapatra2  and Y. S. Valaulikar3

1Department of Mathematics

S. P. K. Mahavidyalaya Sawantwadi, Maharashtra- 416510, India

Email: vpsonalkar@yahoo.com

2Visiting Faculty, Department of Mathematics

Centurion University, Pitamahal, Rayagada - 765001, Odisha, India

Email: anm999@gmail.com

3Department of Mathematics

Goa University, Goa - 403206, India

Email: ysv@unigoa.ac.in; ysvgoa@gmail.com

(Received: March 13, 2020; Revised: August 17, 2020)

 

 

In this paper, we prove the Hyers-Ulam (HU) stability of the first and second order partial differential equations: ux(x,t)+K(x, u(x,t))=0 and uxx(x,t)+F(x,u)ux(x,t)+H(x,u)=0 respectively.

 

2010 Mathematics Subject Classifications: 26D10; 35B35; 34K20; 39B52.

Keywords and phrases: Hyers Ulam stability, Partial differential equations, Banach Contraction Principle.