K T Joseph
Articles written in Proceedings – Mathematical Sciences
Volume 99 Issue 2 August 1989 pp 181-190
We consider initial boundary value problems for certain nonlinear scalar parabolic equations. A formula for the unique classical solution by Hopf-Cole transformations is obtained and the asymptotic behaviour of the solution as time goes to ∞ is studied.
Volume 102 Issue 1 April 1992 pp 29-47
In this paper we consider scalar convex conservation laws in one space variable in a strip
Volume 109 Issue 4 November 1999 pp 401-409
This paper studies a special 3 by 3 system of conservation laws which cannot be solved in the classical distributional sense. By adding a viscosity term and writing the system in the form of a matrix Burgers equation an explicit formula is found for the solution of the pure initial value problem. These regularized solutions are used to construct solutions for the conservation laws with initial conditions, in the algebra of generalized functions of Colombeau. Special cases of this system were studied previously by many authors.
Volume 115 Issue 4 November 2005 pp 509-517
In this paper we study the asymptotic behaviour of solutions of a system of