Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion. (March 2020) - Bedjaoui, N.; Correia, J.M.C.; Mammeri, Y.
Abstract: We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form u t + f ( u ) x = ε u x x − δ ( | u x x | n ) x . Convergence of the solutions { u ε, δ } to the entropy weak solution of the hyperbolic limit equation u t + f ( u ) x = 0, for all real numbers 1 ≤ n ≤ 2 is proved if δ = o ( ε 3 n − 1 2 ; ε 5 n − 1 2 ( 2 n − 1 ) ) .