Global solutions to viscous hamilton-jacob1 equations with irregular initial data

We invcestigat, the existcnce and uniqueness of non-negative weak solutions to with initial data in the spacc of bounded and non-negative measures when and in whcn provided that q is large enougli. Non-cxistc.ncc of solutions with Dirac masses as initial data is also shown when We finally study the large time behaviour of the L1-nor111 of t,he solutions to the Cauchy problem, thereby extending previous results to ii wider class of initial data. One main step in our approach is the derivation of drcay estimates of theL∞-norm of the gradient of