V. I. Tsurkov 01.1998 p. 88, language: английский  Аннотация The subject of this book is the problem of unboundedness of classical solutions to conservation laws, i.e., to quasilinear hyperbolic sets of first-order differential equations. A smooth solution to the problem with initial conditions (the Cauchy problem) is known to exist only in a bounded band. At some instant of time, the derivatives can become infinite. There are two causes of this phenomenon. One of them is connected with the fact that eigenvalues of the system matrix depend nonlinearly on unknown solutions. The case in point is the formation of the discontinuity or, speaking in terms of gas dynamics, shock wave, which is illustrated by the example of the simplest Hopf equation. The second cause is the lack of integrating factors of Pfaffian forms of left eigenvectors of the system matrix, which can take place for systems of order greater than or equal to three.  Ключевые слова quasilinear hyperbolic systems of first-order differential equations, Cauchy problem, unboundedness, catastrophe   Полный текст     в неизвестном формате