Global wellposedness for quasi‐linear symmetric hyperbolic systems with regularized coefficients

Abstract

AbstractFollowing the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasi‐linear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a regularizing function. In the case of unbounded regularized coefficients, local existence of classical solutions is proved, as well as uniqueness and regularity of (not necessarily existing) global weak solutions with initial value in a Sobolev space. As the regularizing function tends to Dirac's δ, local‐in‐time convergence to the classical solution of the non‐regularized problem is proved.