Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

SEMINAR

 

Speaker

:

 Dr. Shyam Sundar Ghoshal
Affiliation : TIFR Centre for Applicable Mathematics, Bangalore.

Subject Area

:

Mathematics

 

Venue

:

Department of Mathematics, Lecture Hall I

 

Time

:

2.30 p.m.-3.30 p.m.

 

Date  

:

May24, 2012 (Thursday)

Title

:

"Structure of the entropy solution of a scalar conservation law with strict convex flux"
Abstract

:

We prove the Structure Theorem of the entropy solution. Furthermore we obtain the shock regions each of which represents a single shock at infinity. Using the structure Theorem we construct initial data $u_0\in C_c^\f$ for which the solution exhibits infinitely many shocks as $t \rightarrow \f$. Also we have generalized the asymptotic behavior (the work of Dafermos, Liu, Kim) of the solution and obtain the rate of decay of the solution with respect to the $N$-wave. Basic ingredients in the proof of these results are Lax-Oleinik explicit formula and generalized characteristics which was introduced by Dafermos. This is joint work with Adimurthi and G.D. Veerappa Gowda.