Prolongation of classical solutions and singularities of generalized solutions
Conditions for existence of global classical solutions or formation of singularities in solutions of Cauchy problems for general partial differential equations of first order are obtained. The reason why properties of singularities may depend on the type of equations (Hamilton-Jacobi equations, conservation laws) is discussed. The Rankin- Hugoniot's condition for a single quasilinear equation is solved.
scientific article; zbMATH DE number 4190248
scientific article