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

Abstract

This paper concerns the asymptotic behavior of solutions to the Cauchy problem of a class of coupled semilinear parabolic systems with gradient terms. Using the energy comparison method and comparison principle, the blow-up theorem of Fujita type is established and the critical Fujita curve is formulated by spacial dimension, the behavior of the coefficient of the gradient term at infinity.

Fujita-type theorems for a class of coupled semilinear parabolic systems with gradient terms

“…Let us turn to proving Theorem 1.2. From Lemma 3.1, Remark 3.1, the Hölder inequality, and Lemma 3.6 in [24], it follows that The same argument as the proof of Theorem 1.1 shows that (u, v) must blow up in a finite time.…”

“…Na et al [24] showed that the critical Fujita curve for problem (1.1)-(1.3) with λ 1 = λ 2 = 0 and nonnegative b is…”

Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy

“…Such results revealed the relationship between the asymptotic behavior of the solutions to nonlinear partial differential equations and the exponents of nonlinear internal sources. Different extension directions, such as different types of parabolic equations and systems in various of geometries with or without degeneracies or singularities, have been obtained since then, see the survey papers [8,18] and also the recent papers [2,19,22,29,30,34,35,36,38]. Among them, the Cauchy problem of the following coupled semilinear parabolic system was studied…”