BIFURCATIONS OF SHOCK-WAVES FOR VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS OF ONE SPACE VARIABLE

We study the generation and propagation of shock waves for viscosity s olutions to the Cauchy problem for Hamilton-Jacobi equations in one sp ace variable. Applying the method of characteristics, we obtain multi- valued solutions. In our previous paper we have given the generic clas sification of the multi-valued solutions around the singularities. In this paper we solve the local Riemann problem using the normal form of the multivalued-solution to construct the corresponding viscosity sol ution.