Critical extinction exponent for a doubly degenerate non-divergent parabolic equation with a gradient source

Doubly Degenerate Parabolic Equation with Time-Dependent Gradient Source and Initial Data Measures

“…erefore, (8)-(11) follow from (53), (20), (26), (28), and (29), provided that we can indeed find a quantitative estimates below t 3 ≥ T 0 . We may assume t 3 < T * , since the estimate is otherwise trivial.…”

“…However, the existence of solutions for initial data measures was left open. In the bounded domain, the critical extinction exponent, the existence, and uniqueness of weak solutions were studied [28,29]. Weng [30] established the existence and stability of weak solutions to the double degenerate evolutionary p(x)-Laplacian equation.…”

“…Inserting (33) and (36) into (35), we obtain (28). It is left to choose β and r such that (34), (37), and (38) hold.…”

Extinction Phenomenon and Decay Estimate for a Quasilinear Parabolic Equation with a Nonlinear Source

“…Extinction phenomenon, as one of the most remarkable properties that distinguish nonlinear parabolic problems from the linear ones, attracted extensive attentions of mathematicians in the past few decades (see [5][6][7][8][9][10][11][12][13][14][15][16] and the references therein). Especially, many authors devoted to concern with the extinction behavior of the following parabolic problem…”

Global Existence and Extinction Singularity for a Fast Diffusive Polytropic Filtration Equation with Variable Coefficient

“…subject to various assumptions (see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein). For the case s � 0, the authors in [24][25][26] concerned with the global existence and blow-up properties of the solutions to problem (4) with m � 1 and p ≥ 2.…”