Hyperbolic Systems of Balance Laws in One-Space Dimension
Chapters VII-XVI will be devoted to the study of systems of balance laws in one space dimension. This narrowing of focus is principally dictated by necessity: At the present time the theory of multidimensional systems is terra incognita, replete with fascinating problems. In any event, the reader should bear in mind that certain multidimensional phenomena, with special symmetry, such as wave focussing, may be studied in the context of the one-space-dimensional theory. We will return to several space dimensions in Chapter XVII. This chapter introduces many of the concepts that serve as foundation of the theory of hyperbolic systems of balance laws in one space dimension: strict hyperbolicity; Riemann invariants and their relation to entropy; simple waves; genuine nonlinearity and its role in the breakdown of classical solutions. In order to set the stage, the chapter opens with the presentation of a number of illustrative examples of hyperbolic systems of balance laws in one space dimension, arising in physics or other branches of science and technology.
KeywordsClassical Solution Hyperbolic System Characteristic Family Simple Wave Characteristic Speed
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