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Summer Research Fellowship Programme of India's Science Academies

STUDY OF TWO IMPORTANT LINEAR PARTIAL DIFFERENTIAL EQUATIONS

Shreyas M.S

Pondicherry University, Kalapet , Puducherry, PIN: 605014

Dr. Venky Krishnan

TIFR CAM, Sharadanagar, Chikkabommasandra, GKVK Post Office, Yelahanka New Town, Bengaluru, PIN: 560065, Karnataka

Abstract

The main aim of my project is to study the two important linear partial differential equations, namely transport equation and Laplace equation, their properties and their fundamental solutions, harmonic functions and their properties. With the remarkable advance made in various branches of sciences, engineering and technology, the study of differential equations is essential. An understanding of subjects like physics, mathematical models, meechanics, heat transfer, waves and electromagnetic is necessary to find solutions with differential equations. So mathematical knowledge and some ideas about differential equation are essential for the sciences, including engineering. The study of differential equations is a wide field in pure applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types.

Keywords: transport equation, Laplace equation, harmonic functions

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