共查询到20条相似文献,搜索用时 15 毫秒
1.
W.Y. Chan 《Journal of Computational and Applied Mathematics》2011,235(13):3831-3840
For the problem given by uτ=(ξrumuξ)ξ/ξr+f(u) for 0<ξ<a, 0<τ<Λ≤∞, u(ξ,0)=u0(ξ) for 0≤ξ≤a, and u(0,τ)=0=u(a,τ) for 0<τ<Λ, where a and m are positive constants, r is a constant less than 1, f(u) is a positive function such that limu→c−f(u)=∞ for some positive constant c, and u0(ξ) is a given function satisfying u0(0)=0=u0(a), this paper studies quenching of the solution u. 相似文献
2.
L.E. Payne 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):971-1014
This paper deals with the blow-up of the solution to a semilinear second-order parabolic equation with nonlinear boundary conditions. It is shown that under certain conditions on the nonlinearities and data, blow-up will occur at some finite time and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
3.
Fei Liang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2189-2198
This paper deals with the blow-up for a system of semilinear r-Laplace heat equations with nonlinear boundary flux. It is shown that, under certain conditions on the nonlinearities and data, blow-up will occur at some finite time, and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
4.
This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also. 相似文献
5.
Blow-up for semilinear parabolic equations with nonlinear memory 总被引:4,自引:0,他引:4
In this paper, we consider the semilinear parabolic
equation
with homogeneous Dirichlet boundary conditions, where
p, q are
nonnegative constants. The blowup criteria and the blowup rate
are obtained. 相似文献
6.
Let G=(V,E) be a locally finite connected weighted graph, and Δ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut=Δu + f(u) on G. The blow-up phenomenons for ut=Δu + f(u) are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time. 相似文献
7.
N. Mavinga 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5171-5188
We study the existence of (generalized) bounded solutions existing for all times for nonlinear parabolic equations with nonlinear boundary conditions on a domain that is bounded in space and unbounded in time (the entire real line). We give a counterexample which shows that a (weak) maximum principle does not hold in general for linear problems defined on the entire real line in time. We consider a boundedness condition at minus infinity to establish (one-sided) L∞-a priori estimates for solutions to linear boundary value problems and derive a weak maximum principle which is valid on the entire real line in time. We then take up the case of nonlinear problems with (possibly) nonlinear boundary conditions. By using comparison techniques, some (delicate) a priori estimates obtained herein, and nonlinear approximation methods, we prove the existence and, in some instances, positivity and uniqueness of strong full bounded solutions existing for all times. 相似文献
8.
M. Kbiri Alaoui A. Souissi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):5863-5875
The paper deals with the existence of solutions of some unilateral problems in the framework of Orlicz spaces. 相似文献
9.
Kevin McLeod Albert Milani 《NoDEA : Nonlinear Differential Equations and Applications》1996,3(1):79-114
We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+. 相似文献
10.
Lamia Mâatoug 《Journal of Functional Analysis》2006,233(2):583-618
We study the existence and the asymptotic behavior of positive solutions for the parabolic equation on D×(0,∞), where is a some unbounded domain in and V belongs to a new parabolic class J∞ of singular potentials generalizing the well-known parabolic Kato class at infinity P∞ introduced recently by Zhang. We also show that the choice of this class is essentially optimal. 相似文献
11.
In this paper, an initial boundary value problem related to the equation
12.
Adrian Constantin Joachim Escher 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(1):91-118
We present some results on the global existence of classical solutions for quasilinear parabolic equations with nonlinear
dynamic boundary conditions in bounded domains with a smooth boundary. 相似文献
13.
Giuseppe M. Coclite Gisèle R. Goldstein Jerome A. Goldstein 《Journal of Differential Equations》2009,246(6):2434-3971
Of concern is the nonlinear uniformly parabolic problem
14.
15.
16.
We investigate the non-existence of solutions to a class of evolution inequalities; in this case, as it happens in a relatively small number of blow-up studies, nonlinearities depend also on time-variable t and spatial derivatives of the unknown. The present results, which in great part do not require any assumption on the regularity of data, are completely new and shown with various applications. Some of these results referring to the problem ut=Δu+a(x)|u|p+λf(x) in RN, t>0 include the non-existence results of positive global solutions obtained by Fujita and others when a≡1 and f≡0, Bandle-Levine and Levine-Meier when a≡|x|m and f≡0, Pinsky when either f≡0 or f?0 and λ>0, Zhang and Bandle-Levine-Zhang when a≡1 and λ=1. 相似文献
17.
We study the asymptotic behavior of Lipschitz continuous solutions of nonlinear degenerate parabolic equations in the periodic setting. Our results apply to a large class of Hamilton–Jacobi–Bellman equations. Defining Σ as the set where the diffusion vanishes, i.e., where the equation is totally degenerate, we obtain the convergence when the equation is uniformly parabolic outside Σ and, on Σ, the Hamiltonian is either strictly convex or satisfies an assumption similar of the one introduced by Barles–Souganidis (2000) for first-order Hamilton–Jacobi equations. This latter assumption allows to deal with equations with nonconvex Hamiltonians. We can also release the uniform parabolic requirement outside Σ. As a consequence, we prove the convergence of some everywhere degenerate second-order equations. 相似文献
18.
In this paper, we develop a viscosity method for homogenization of Nonlinear Parabolic Equations constrained by highly oscillating obstacles or Dirichlet data in perforated domains. The Dirichlet data on the perforated domain can be considered as a constraint or an obstacle. Homogenization of nonlinear eigen value problems has been also considered to control the degeneracy of the porous medium equation in perforated domains. For the simplicity, we consider obstacles that consist of cylindrical columns distributed periodically and perforated domains with punctured balls. If the decay rate of the capacity of columns or the capacity of punctured ball is too high or too small, the limit of u? will converge to trivial solutions. The critical decay rates of having nontrivial solution are obtained with the construction of barriers. We also show the limit of u? satisfies a homogenized equation with a term showing the effect of the highly oscillating obstacles or perforated domain in viscosity sense. 相似文献
19.
Michael Winkler 《Journal of Differential Equations》2003,192(2):445-474
We study nonglobal positive solutions to the Dirichlet problem for ut=up(Δu+u) in bounded domains, where 0<p<2. It is proved that the set of points at which u blows up has positive measure and the blow-up rate is exactly . If either the space dimension is one or p<1, the ω-limit set of consists of continuous functions solving . In one space dimension it is shown that actually as t→T, where w coincides with an element of a one-parameter family of functions inside each component of its positivity set; furthermore, we study the size of the components of {w>0} with the result that this size is uniquely determined by Ω in the case p<1, while for p>1, the positivity set can have the maximum possible size for certain initial data, but it may also be arbitrarily close to the minimal length π. 相似文献
20.
This paper deals with the blow-up behavior of radial solutions to a parabolic system multi-coupled via inner sources and boundary flux. We first obtain a necessary and sufficient condition for the existence of non-simultaneous blow-up, and then find five regions of exponent parameters where both non-simultaneous and simultaneous blow-up may happen. In particular, nine simultaneous blow-up rates are established for different regions of parameters. It is interesting to observe that different initial data may lead to different simultaneous blow-up rates even with the same exponent parameters. 相似文献