Boundary estimates for certain degenerate and singular parabolic 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...

Carleman Estimates and Null Controllability of Degenerate/singular Parabolic Systems

We study null controllability properties for parabolic coupled systems with degeneracy and singularity occurring in the interior of the spatial domain. This article is the first to consider a problem with singular coupling terms; previous result cannot be adapted to this situation. In particular, we focus on the well posedness of the problem and then we prove Carleman estimates for the associat...

Editorial Harnack's Estimates: Positivity and Local Behavior of Degenerate and Singular Parabolic 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...

Gradient estimates for degenerate quasi-linear parabolic equations

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients infinitesimally form bounded with respect to the Laplacian we obtain Lq-estimates for the gradients of solutions, and for the lower order coefficients from a Kato-type class we show that the solutions are Lipschitz continuous with respect to the space var...