Abstract:

The Cauchy problem of the equation ut-div(|Dum|p-2Dum)=t-σuq,is studied, where m>0, p>1. This equation is called doubly nonlinear parabolic equation, since the principal part may be doubly degenerate or doubly singular related to the parameters m, p. By a priori estimates and compactness methods, and fine classifications to parameters m, p, we obtain the optimal existence of solutions of the equation with initial data measures are obtained.

Key words: Cauchy problem; doubly nonlinear equation; time-dependent source; measures as initial data