Hyperbolic systems with relaxation: characterization of stiff well-posedness and asymptotic expansions
The Cauchy problem for linear constant-coefficient hyperbolic systems ut + ∑j A(j)uxj = (1/δ)Bu + Cu in d space dimensions is analyzed. Here (1/δ)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non-trivial null-space. A concept of stiff well-posedness is introduced that ensures solution estimates independent of 0 < δ 1. Stiff well-posedness is charact