Self-Similar Subsolutions and Blowup for Nonlinear Parabolic Equations

For a wide class of nonlinear parabolic equations of the form utyDus F u, =u., we prove the nonexistence of global solutions for large initial data. We also estimate the maximal existence time. To do so we use a method of comparison with suitable blowing up self-similar subsolutions. As a consequence, we improve several known results on utyDusu p, on generalized Burgers’ equations, and on other semilinear equations. This method can also apply to degenerate equations of porous medium type and provides a unified treatment for a large class of problems, both semilinear and quasilinear.