Radially Symmetric Weak Solutions for a Quasilinear Wave Equation in Two Space Dimensions

Hermano Frid | Dias, João Paulo

Keywords: quasilinear hyperbolic systems | conservation laws | compensated compactness | entropies | Young measures

We prove the convergence of the radially symmetric solutions to the Cauchy problem for the viscoelasticity equations (null) as $\ve\to0$, with radially symmetric initial data $\phi^\ve(x,0)=\phi_0^\ve(r)$, $\phi_t^\ve(x,0)=\phi_1^\ve(r)$, $r=(x_1^2+x_2^2)^{1/2}$, where $\phi_{0r}^\ve\wto{\phi}_{0r}$, $\phi_1^\ve\wto{\phi}_1$, to a weak solution of the Cauchy problem for the corresponding limit equation with $\ve=0$, and initial data $\phi(x,0)=\phi_0(r)$, $\phi_t(x,0)=\phi_1(r)$. Our analysis is based on energy estimates and the method of compensated compactness closely following D.~Serre and J.~Shearer (1993).

Anexos:

• diasfrid1.pdf