Arrondissement de Rouen, Francia
We investigate the existence and the stability of the solutions of a nonlinear evolution equation with a local quadratic term with respect to the gradient of the type g(u)|Du|2 and for measure initial data. We extend the notion of renormalized solutions for this problem. Under a natural condition on the convergence of the initial data, we prove the compactness of the truncation of solutions in the energy space. Then we show that the integrability of g at infinity is a necessary and sufficient condition for the stability of the problem with respect to general measure data, as well as for the existence of renormalized solutions.
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