Titlebook: Hyperbolic Conservation Laws in Continuum Physics; Constantine M. Dafermos Book 20052nd edition Springer-Verlag Berlin Heidelberg 2005 Ent

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The Cauchy Problem,om smooth initial values, spontaneously develop discontinuities; hence in general only weak solutions may exist in the large. Next, weak solutions to the Cauchy problem fail to be unique. One does not have to dig too deep in order to encounter these difficulties. As shown in Sections 4.2 and 4.4, th

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Hyperbolic Systems of Balance Laws in One-Space Dimension,ted by necessity: At the present time the theory of multidimensional systems is terra incognita. Eventually, research should turn to that vastly unexplored area, which is replete with fascinating problems. In any event, the reader should bear in mind that certain multidimensional phenomena, with spe

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Admissible Shocks,ere encountered again, briefly, in Section 3.1, where the governing Rankine-Hugoniot condition was recorded..Since shock fronts have codimension one, important aspects of their local behavior may be investigated, without loss of generality, within the framework of systems in one-space dimension. Thi

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Admissible Wave Fans and the Riemann Problem,lar solutions, which stay constant along straight-line rays emanating from some focal point in space-time. Such solutions depict a collection of waves converging to the focal point and interacting there to produce a jump discontinuity which is in turn resolved into an outgoing wave fan..This chapter

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The Random Choice Method,ly defined, admissible . solutions to the Cauchy problem for strictly hyperbolic systems of conservation laws, under initial data with small total variation. The solution is obtained as the limit of a sequence of approximate solutions that do not smear shocks. Solutions to the Riemann problem, discu

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