CONTINUATION AFTER BLOW-UP OF SOLUTIONS OF NONLINEAR HEART EQUATIONS

We study the possible continuation of solutions of some quasilinear he at equation with power nonlinearities after the blow-up time. In a cer tain parameter range we find a phenomenon of nontrivial continuation w here the region of infinite temperature is bounded and propagates with finite speed (incomplete blow-up). This gives rise to a new free boun dary problem. In the supercritical range we construct self-similar sol utions which blow-up at a finite time T and become again bounded for t > T, so-called peaking solutions. Otherwise we End complete blow-up f or a rather general class of initial data.