[PDF] Top 20 Some Features for Blow-up Solutions of a Nonlinear Parabolic Equation

... Precisely, It has been proved that if δ ≥ 2 then there exists solutions of (1) which are “Type 2” and if 0 < δ < 2 then u is “Type 1”. (See [3], [4], [5], [7], [8], [9], [10], [11] and so force.) Our purpose ... See full document

... the blow-up time t ∗ if the blow-up does really occur together with a criterion for getting a ...a blow-up cannot ...the blow-up time of solutions in a ... See full document

... [] and in the physical phenomena such as diffusion and convection of matter. One of the main features of equation (.) is the strong degeneracy due to the lack of diffusion in the y- direction. We restrict ... See full document

... and blow- up properties of solutions for nonlinear parabolic equations, especially the initial bound- ary value problems with nonlocal terms in equations or boundary conditions, we ... See full document

... on blow-up solutions for nonlinear parabolic equation with nonlocal source by Levine in [], many efforts have been made devoted to the study of blow-up properties ... See full document

... and blow-up for nonlinear parabolic equations have been extensively investigated by many authors in the last decades (see [1–6] and the references ...the blow-up time in ... See full document

... the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary ...The blow-up and global existence ... See full document

... The nonlinear beam equation is a class of fourth-order partial differential equations ap- pearing in different physical settings (see [26, 27] for a review), and it models the weak interactions of dispersive ... See full document

... where Ω ⊂ R n is a bounded domain with smooth boundary ∂Ω in order that the divergence theorem can be applied. ν is the unit normal vector pointing toward the exterior of Ω and p > 0. Here, g represents the kernel of ... See full document

... The authors established an exponential rate of decay. This latter result has been improved by Cavalcanti and Oquendo [18] and Berrimi and Messaoudi [19]. In their work, Cavalcanti and Oquendo [18] considered the ... See full document

... the Laplacian. The parameter m > 0. In fact, Eq. (1.1) is a class of fourth-order partial dif- ferential equations having different physical settings (see [19]). In particular, when d = 1, Eq. (1.1) is called ... See full document

... and blow-up in finite time of solutions for a variety of generalizations of such models have subsequently been investigated in a number of previous works, ...the blow-up properties of ... See full document

... of blow-up in lo- cal or nonlocal ...the solutions of the initial boundary value problem of nonlocal equation ...will blow up in finite time, since the comparison principle, which ... See full document

... abstract nonlinear damped hyperbolic equations appears in many applications to natural sciences, such as the unidirectional propagation of nonlinear longitudinal displacement [1], dynamical longitudinal ... See full document

... In Section 2, we recall some materials given in [8] and [42], which are needed in our proofs. In Section 3, for sake of convenience, we give two important lemmas as well as the detailed proofs. In Section 4, we ... See full document

... This paper is organized as follows. In Section , we determine the blow-up condition of solutions of Eq. (.). In Section , we deal with global existence condition and then conclude that the global ... See full document

... where p > 2, ω, μ > 0. The authors established the global existence theorem and proved that the global solution is uniformly bounded. They also constructed the finite time blow- up of solutions ... See full document

... global solutions while if Nα > 2, there were non-trivial global ...the blow-up phenomenon for the reaction-diffusion equations has been the object of intensive ...Degenerate parabolic ... See full document

... The study for the Cauchy problem of nonlocal nonlinear parabolic equation was pro- posed by Galaktionov et al. [1], in which it was proved that the Cauchy problem (1.1) with m = 1 has a critical ... See full document

... subject to the homogeneous Dirichlet boundary condition. By using the comparison prin- ciple and constructing a self-similar lower solution, they obtained sufficient conditions for global existence and ... See full document