Self-similar subsolutions and blowup for nonlinear parabolic equations

[摘要] For a wide class of nonlinear parabolic equations of the form u(t) - Delta u = F(u, del 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 u(t) - Delta u = u(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. (C) 1997 Academic Press.

[发布日期] 1997-08-01