Book Review: Quasilinear hyperbolic systems, compressible flows, and waves

Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 22 systems of genuinely nonlinear hyperbolic balance laws in 1-D with a strong dissipative term. A diierent method, which combines the div-curl lemma with accretive ope...

Quasilinear Symmetric Hyperbolic Fuchsian Systems in Several Space Dimensions

We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an extension of earlier work by the authors for the same problem in one space dimension.

EXACT BOUNDARY OBSERVABILITY FOR QUASILINEAR HYPERBOLIC SYSTEMS 761 Remark 1

By means of a direct and constructive method based on the theory of semi-global C solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case. Mathe...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows

Resonance for Quasilinear Hyperbolic Equation

git u) = c(8ft(ii), ? = x dt, where c(£) is a piecewise continuous function and h(u) is a smooth positive function whose first derivative does not change signs. The external effect is assumed to be finite; for simplicity, we suppose also that c(£) has compact support. Our main interest is the behavior of nonlinear waves when the resonance occurs, that is, when the characteristic speed f(u) is c...