• G D Veerappa Gowda

      Articles written in Proceedings – Mathematical Sciences

    • Solution of convex conservation laws in a strip

      K T Joseph G D Veerappa Gowda

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      In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t > 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

      Adimurthi G D Veerappa Gowda

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      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.

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