Boundedness and blow up for a semilinear reaction-diffusion system

Existence and nonexistence of global solutions of degenerate and singular parabolic systems

“…and the nonexistence condition given by Theorem 2.4 coincides with the condition found by Escobedo and Herrero in [2], for the system of equations with positive initial data, that is,…”

“…The main result of this section (Theorem 2.4) recovers the result obtained in [7] for the single inequality, that is, when τ 1 = τ 2 and p = q. Moreover, Theorem 2.4 includes as a particular case the result by Escobedo and Herrero [2], which concerns the system of equations under the assumptions that τ 1 = τ 2 = 0 and u 0 , v 0 ≥ 0.…”

“…46) which shows that if C > 0 is sufficiently small and B C denotes the ball of ᐄ of radius C, then 2 The general case can be treated by slight modifications. Applying Hölder inequality to (4.2) we get where can be treated as in the proof of Theorem 2.4.…”

Asymptotic behavior of solutions to a class of coupled semilinear parabolic systems with gradient terms

“…Furthermore, Suzuki [14] considered the Newtonian filtration equation with similar gradient term and got the critical Fujita exponent for some special cases. In 1991, Escobedo and Herrero [2] investigated the coupled semilinear parabolic system (1.1), (1.2), (1.3) in the special case b ≡ 0, and formulated the critical Fujita curve as…”

A Uniqueness Result for a Semilinear Reaction-Diffusion System

“…System (1.1) has been analyzed by several authors in the case of bounded and unbounded domains (cf. [7], [8], [5], [4], [3], etc.). In particular, it has been shown in [3] that problem (1.1), (1.2) always has a classical solution in some strip ST = [0, T) x R with 0 < T < oo.…”