Blow-up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions

Lower bound for the blow-up time for a general nonlinear nonlocal porous medium equation under nonlinear boundary condition

“…Some authors have started to consider the blow-up of these problems under Robin boundary conditions (see [13][14][15][16][17]). In papers [18][19][20][21], the authors studied the blow-up phenomena for the heat equation under nonlinear boundary conditions. Some new results about the nonlinear evolution equations may be founded in [22][23][24].…”

Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions

“…At present, the studies on the blow-up phenomena of parabolic problems mainly focus on homogeneous Dirichlet boundary condition and homogeneous Neumann and Robin boundary conditions [3][4][5][6][7][8][9][10][11][12]. ere are also some works under nonlinear boundary conditions [13][14][15]. Most of these articles are focused on R 3 .…”

Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions

“…Furthermore, it follows from maximum principle [10] and regularity theorem [11] that the solution ( , ) is positive and ( , ) ∈ 3 (Ω × (0, )) ∩ 2 (Ω × (0, )). Many authors have investigated blow-up and global solutions of nonlinear reaction-diffusion equations under nonlinear boundary conditions and have obtained a lot of interesting results (see, e.g., [12][13][14][15][16][17][18][19][20]). To my knowledge, some special cases of (1) have been studied.…”