• G D Veerappa Gowda

Articles written in Proceedings – Mathematical Sciences

• Solution of convex conservation laws in a strip

In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t &gt; 0 and obtain an explicit formula for the solution of the mixed initial boundary value problem, the boundary data being prescribed in the sense of Bardos-Leroux and Nedelec. We also get an explicit formula for the solution of weighted Burgers equation in a strip.

• Formula for a solution ofut +H(u,Du) =g

We study the continuous as well as the discontinuous solutions of Hamilton-Jacobi equationut +H(u,Du) =g in ℝn x ℝ+ withu(x, 0) =u0(x). The HamiltonianH(s,p) is assumed to be convex and positively homogeneous of degree one inp for eachs in ℝ. IfH is non increasing ins, in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous viscosity solutions.

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019