\(L^\infty\) estimates for conservation laws with hyperviscous parabolic terms (Q1601132)

The author considers the question of \(L^\infty\) estimates for hyperbolic conservation laws which are regularized with higher order \((2s\), with \(s\) as integer \(\geq 1)\) parabolic terms. The analysis involves \(L^\infty\) estimates of the associated linear parabolic equation which is studied both on circle and on the line. Given an a priori \(L^\infty\) estimate on the solution, the paper aims at analyzing the behaviour of this estimate as \(s\to\infty\). The paper may be of interest to someone working in the field of nonlinear partial differential equations and their numerical solutions.