A boundary estimate for singular parabolic diffusion equations

A note on critical point and blow-up rates for singular and degenerate parabolic equations

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

Blowup Rate Estimate for a System of Semilinear Parabolic Equations

In this paper, we study the blowup rate estimate for a system of semilinear parabolic equations. The blowup rate depends on whether the two components of the solution of this system blow up simultaneously or not.

Free Boundary Problems for Parabolic Equations

An address delivered at the Ann Arbor meeting of the American Mathematical Society on November 29, 1969, by invitation of the Committee to Select Hour Speakers for Western Sectional Meetings; received by the editors April 9,1969. AMS 1969 subject classifications. Primary 3562, 3578.

Initial - Boundary Value Problems for Parabolic Equations

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data