Singularities of solutions for nonlinear hyperbolic equations of second order

Abstract

We consider the Cauchy problem for nonlinear hyperbolic partial differential equations of second order. Then the Cauchy problem does not generally admit a classical solution in the large, that is to say, singularities generally appear in finite time. The typical example of singularity is “shock wave”. Our problem is to extend the solution beyond the singularities. Though there are many papers concerning this subject, the existence and uniqueness of weak solution is even now unsolved. In this talk we consider the above problem from geometrical point of view.KeywordsWeak SolutionCauchy ProblemContact StructureNonlinear Wave EquationJump DiscontinuityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.