Blow-up in p-Laplacian heat equations with nonlinear boundary conditions

Global existence and blow-up results for p-Laplacian parabolic problems under nonlinear boundary conditions

“…For more than ten years, many authors have discussed the blow-up phenomena of p -Laplacian parabolic problems. We refer the readers to [ 1 – 11 ] and the references therein. In this paper, we intend to study the blow-up phenomena of the following p -Laplacian parabolic problems: In ( 1.1 ), , the spatial region D in ( ) is bounded, ∂D is smooth, is the blow-up time if the blow-up occurs, otherwise , is a function with , , is a positive function, is a positive function, and is a nonnegative function with , .…”

“…The blow-up problems for parabolic equations with nonlinear boundary conditions have been widely investigated in recent years (see, e.g., [ 1 , 6 , 13 – 26 ]). In order to study problem ( 1.1 ), we focus on the papers [ 1 , 16 ], and [ 22 ].…”

“…The blow-up problems for parabolic equations with nonlinear boundary conditions have been widely investigated in recent years (see, e.g., [ 1 , 6 , 13 – 26 ]). In order to study problem ( 1.1 ), we focus on the papers [ 1 , 16 ], and [ 22 ]. In [ 1 ], Ding and Shen considered the following problems: In ( 1.2 ), , the spatial region D in ( ) is bounded and convex, and ∂D is smooth.…”

Blow‐up analysis for a class of nonlinear reaction diffusion equations with Robin boundary conditions

“…However, it may be harder to determine lower bounds for the blow-up time. Over the last few decades, there were many papers devoted to deriving lower bounds for the blow-up time in reaction diffusion problems (see other works [4][5][6][7][8][9][10][11][12] ). To our knowledge, the results of the papers mentioned above always derived the lower bounds by restricting Ω ⊂ R 3 .…”

Upper and lower bounds for the blow-up time in quasilinear reaction diffusion problems

“…At meanwhile, we note that lower bounds for blow-up 4244 JUNTANG DING AND XUHUI SHEN time seem harder to be determined. Since Payne and Scheafer in [17] used a firstorder differential technique and derived a lower bound for blow-up time, the similar idea is also applied in more generalized problems (see [1,[3][4][6][7][8][12][13][14][15][16][18][19]). The direct motivation of this paper comes from [5].…”