Singularities of solutions for nonlinear first order partial differential equations (Q2917452)

From the text: This is a survey on recent results about singularities of solutions for nonlinear first order partial differential equations as applications of the singularity theory of smooth mappings. NEWLINENEWLINEThe author first considers two Cauchy problems for the Hamilton-Jacobi equation and the single conservation law using the classical method of characteristics. Then section 2 surveys the geometric framework for the study of the multi-valued solutions of the Cauchy problem for a general Hamilton-Jacobi equation, section 3 describes recent results on the relation between Legendrian solutions and viscosity solutions for Hamilton-Jacobi equations, and the final section 4 considers singularities of multi-valued solutions for the stationary Hamilton-Jacobi equation.