Radially symmetric weak solutions for a quasilinear wave equation in two space dimensions

We prove the convergence of the radially symmetric solutions to the Cauchy problem for the viscoelasticity equations as →0, with radially symmetric initial data , , , where , , to a weak solution of the Cauchy problem for the corresponding limit equation with =0, and initial data φ(x,0)=φ0(r), φt(x,0)=φ1(r). Our analysis is based on energy estimates and the method of compensated compactness closely following Serre and Shearer (Convergence with physical viscosity for nonlinear elasticity, 1993, unpublished).