Finite volume schemes for nonlinear parabolic problems: another regularization method
First order partial functional differential equations with unbounded delay.
Formes bilinéaires compatibles avec un système hyperbolique et problème de Cauchy
Fundamental solutions and singular shocks in scalar conservation laws.
We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks...