Date & Time: Thursday, January 15, 2009, 16:00-17:30.
Venue: Room 215
Title: Introduction to Scalar Conservation Laws
Speaker: S. Baskar, IIT Bombay
Abstract: This is the first talk in a Lecture Series on Hyperbolic Conservation Laws.
More about the series:
Hyperbolic conservation laws are time dependent, first order partial differential equations. This type of equations occur very frequently in practical applications. The main difficulty in dealing with such equations is that, even if we start with a smooth initial data, the solution may develop discontinuities in finite time. Because of its importance in applications and difficulty in obtaining solutions, this type of problems attracted mathematicians and engineers, and is one of the most active areas of research at present.
We are planning to give a series of lectures on Conservation laws, spread over a period of four to six months. These lectures do not assume any knowledge of Partial differential equations as we start from the basics, and hence are accessible to MSc students also. These lectures will eventually introduce a few M.Sc projects and Ph.D. topics. By the end of these lectures one can start reading research papers and work in this field.
The following topics are the main focus of these lectures.
- Basic definitions and examples
- Loss of regularity of a solution
- Review of distribution theory
- Admissible solutions
- Some approximations (Vanishing viscosity method, Numerical approximations)
- Convergence of the approximations using tools like Total variation boundedness, Compensated compactness theory.