Blow-up rates for parabolic systems

Improved conditions for single-point blow-up in reaction–diffusion systems

“…As for the case of monotone in time solutions, it seems that the known proofs of (1.7) for systems (see e.g. [4]) usually require δ = 1. Also we recall that non-equidiffusive parabolic systems are often much more involved, both in terms of behavior of solutions and at the technical level (cf.…”

“…In this paper, we consider nonnegative solutions of the following reaction-diffusion system: As for the functions F and G, we assume that 4) and that system (1.2) is cooperative, i.e. :…”

Global existence from single-component $L_{p}$ estimates in a semilinear reaction-diffusion system

“…Indeed it is known (see [4], [6], [3], [5], [18]) that for large classes of initial data, the blow-up rate of nonglobal solutions of (1.1) is of the order…”

Unique solutions for a new coupled system of fractional differential equations

“…First, we list the following hypotheses A lot of boundary value problems of coupled systems involving fractional differential equations have been investigated extensively, see the works and the references therein. Different boundary conditions of coupled systems can be found in the discussions of some problems such as Sturm-Liouville problems and some reaction-diffusion equations (see [26,27]), and they have some applications in many fields such as mathematical biology (see [28,29]), natural sciences and engineering; for example, we can see beam deformation and steady-state heat flow [30,31] and heat equations [14,32,33]. So nonlinear coupled systems subject to different boundary conditions have been paid much attention to, and the existence or multiplicity of solutions for the systems has been given in literature, see [4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24][25] for example.…”