Indian Institute of Technology Bombay
Mathematics Association of IIT Bombay and Bombay Mathematical Colloquium


Abstract 
The aim of this lecture is to provide a glimpse into mathematical theory of waves. We shall explain a class of mathematical models derived from conservation laws. One of the most outstanding features of the nonlinear theory is the breaking of waves into shock waves. Waves are described in terms of functions u(x, t) of position x and time t that describe density of a quantity. One of the important models involves the Burger's inviscid equation relating u with its derivatives. In this simple framework where the governing equation is considered as a conservation law, the shock waves appear as discontinuities in u(x, t). A few illuminating examples will be explained and extension of these ideas to quasilinear systems of partial differential equations will be touched upon. The lecture will assume only basics of Calculus and ordinary differential equations. 
About the speaker 
Prof. V. D. Sharma is a distinguished teacher and researcher serving
in the Mathematics Department of IIT Bombay since 1988. He graduated
from the Banaras Hindu University in 1972. He has been working for more
than three decades in several areas of applied mathematics, for
example, quasilinear systems of partial differential equations,
nonlinear gasdynamic waves, shallow water waves, mathematical methods,
dynamics of
relaxing, radiating and
electrically conducting fluids and two phase flows.
He is a fellow of the National Academy of Sciences and Indian National Science Academy. He has won the prestigious M. N. Saha and C. L. Chandna awards for his outstanding contributions to teaching and research in mathematics. He is also a recepient of the best teacher award of IIT Bombay. 
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