Gradient blowup rate for a viscous Hamilton–Jacobi equation with degenerate diffusion

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$-Laplacian diffusion

“…The large time behavior of global solutions in bounded or unbounded domains has been studied in [16,25,15,5,4,14]. Concerning the asymptotic description of singularities, results on the gradient blow-up rate in one space dimension can be found in [3,26,27]. On the other hand, in any space dimension, it is known [2] that gradient blow-up can take place only on the boundary, i.e.…”

Non-Self-Similar Dead-Core Rate for the Fast Diffusion Equation with Dependent Coefficient

“…Lemma 2. Let ∈ 2 (0, ∞) be a solution of the stationary equation of (8): (14) such that > 0, ≥ 0, and is polynomially bounded. Then = 0 .…”

“…By an integration, we end up with that ( ) = + 2 for ∈ (0, ∞) for some constants and . Next, we plug the expression ( ) = ( + 2 ) 1/ into (14). Then we can easily derive that…”

“…Other singularity formation mechanisms in related reactiondiffusion equations and reaction-convection equations, such as type II blowup and gradient blowup, also exhibit non-selfsimilar behaviours, respectively. We refer to [11,12] for type II blowup and to [13][14][15][16][17][18][19][20][21] for gradient blowup for recent related results.…”

Single blowup point for a semilinear reaction‐diffusion system

“…Indeed, in , Li and Souplet studied single point gradient blowup. And the mathematical study of the blowup rate of gradient blowup and other aspects were carried out in and so on.…”