Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system
Alexander Anatol'evich Zlotnik,
Boris Nikolaevich Chetverushkin
Abstract:The Cauchy problems are studied for a first-order multidimensional symmetric linear hyperbolic system of equations with variable coefficients and its singular perturbations that are second-order strongly parabolic and hyperbolic systems of equations with a small parameter $\tau>0$ multiplying the second derivatives with respect to $x$ and $t$. The existence and uniqueness of weak solutions of all three systems and $\tau$-uniform estimates for solutions of systems with perturbations are established. Estimate… Show more
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