On certain nonlinear parabolic equations with singular diffusion and data in $L^1$
Concepción García Vázquez, Francisco Ortegón Gallego · Communications on Pure & Applied Analysis · 2005
An existence result is established for a class of nonlinearparabolic equations having a coercive diffusion matrix blowing-upfor a finite value of the unknown, a second hand $f\in L^1(Q)$,and an initial data $u_0\in L^1(\Omega)$. We develop a techniquewhich relies on the notion of a renormalized solution and anadequate regularization in time for certain truncation functions.Some uniqueness results are also shown under additionalhypotheses.