共查询到20条相似文献,搜索用时 453 毫秒
1.
Tor A. Kwembe Zhenbu Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3078-3091
In this paper, we consider a weak coupled semilinear parabolic system with general Wentzell boundary condition. We prove the well-posedness of the problem and derive different conditions in terms of the powers of the nonlinear terms under which the global solution exists and finite time blow-up occurs. 相似文献
2.
This paper deals with the Dirichlet problem for a parabolic system with localized sources. We first obtain some sufficient conditions for blow-up in finite time, and then deal with the possibilities of simultaneous blow-up under suitable assumptions. Moreover, when simultaneous blow-up occurs, we also establish the uniform blow-up profiles in the interior and estimate the boundary layer. 相似文献
3.
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
4.
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
5.
This paper deals with a class of nonlinear parabolic problems in divergence form whose solutions, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to establish conditions on the data sufficient to guarantee blow-up of solution at some finite time τ, conditions to ensure that the solution remains bounded as well as conditions to derive some explicit exponential decay bounds for the solution and its derivatives. 相似文献
6.
We determine the critical blow-up exponent for a Keller-Segel-type chemotaxis model, where the chemotactic sensitivity equals some nonlinear function of the particle density. Assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution. Furthermore, we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails. 相似文献
7.
We study numerical approximations to solutions of a system of two nonlinear diffusion equations in a bounded interval, coupled
at the boundary in a nonlinear way. In certain cases the system develops a blow-up singularity in finite time. Fixed mesh
methods are not well suited to approximate the problem near the singularity. As an alternative to reproduce the behaviour
of the continuous solution, we present an adaptive in space procedure. The scheme recovers the conditions for blow-up and
non-simultaneous blow-up. It also gives the correct non-simultaneous blow-up rate and set. Moreover, the numerical simultaneous
blow-up rates coincide with the continuous ones in the cases when the latter are known. Finally, we present numerical experiments
that illustrate the behaviour of the adaptive method. 相似文献
8.
This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions. 相似文献
9.
THEBLOW┐UPPROPERTYFORASYSTEMOFHEATEQUATIONSWITHNONLINEARBOUNDARYCONDITIONSLINZHIGUI,XIECHUNHONGANDWANGMINGXINAbstract.Thispap... 相似文献
10.
This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs. 相似文献
11.
This paper studies heat equations with inner absorptions and coupled boundary fluxes of mixed-type nonlinearities. At first, the critical exponent is obtained, and simply described via a characteristic algebraic system introduced by us. Then, as the main results of the paper, three blow-up rates are established under different dominations of nonlinearities for the one-dimensional case, and represented in another characteristic algebraic system. In particular, it is observed that unlike those in previous literature on parabolic models with absorptions, two of the multiple blow-up rates obtained here do depend on the absorption exponents. In the known works, the absorptions affect the blow-up criteria, the blow-up time, as well as the initial data required for the blow-up of solutions, all without changing the blow-up rates. To our knowledge, this is the first example of absorption-dependent blow-up rates, exploiting the significant interactions among diffusions, inner absorptions and nonlinear boundary fluxes in the coupled system. It is also proved that the blow-up of solutions in the model occurs on the boundary only. 相似文献
12.
We consider the blow-up of solutions of equations of the form
by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur. 相似文献
ut=div(ρ(|∇u|2) grad u)+f(u)
13.
Yusuke Yamauchi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5008-5014
We present a new upper bound of the life span of positive solutions of a semilinear heat equation for initial data having positive limit inferior at space infinity. The upper bound is expressed by the data in limit inferior, not in every direction, but around a specific direction. It is also shown that the minimal time blow-up occurs when initial data attains its maximum at space infinity. 相似文献
14.
In this paper, we consider the dissipative Camassa–Holm equation with arbitrary dispersion coefficient and compactly supported initial data. We demonstrate the simple conditions on the initial data that lead to finite time blow-up of the solution in finite time or guarantee that the solution exists globally. Also, propagation speed for the equation under consideration is investigated. 相似文献
15.
Xueli BaiShuangshuang Zhou Sining Zheng 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2508-2514
This paper studies the Cauchy problem for the fast diffusion equation with a localized reaction. We establish the Fujita type theorem to the problem, and then obtain the diffusion-independent blow-up rate for the non-global solutions. Moreover, we prove that the blow-up set for the problem consists of a single point under large initial data. These conclusions are quite different from those for the slow diffusion case. 相似文献
16.
带非局部源的退化半线性抛物方程的解的爆破性质 总被引:1,自引:0,他引:1
This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation
u
t
− (x
a
u
x
)
x
=∫
0
a
f(u)dx in (0,a) × (0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under
appropriate hypotheses, the global existence and blow-up in finite time of positve solutions are obtained. It is also proved
that the blow-up set is almost the whole domain. This differs from the local case. Furthermore, the blow-up rate is precisely
determined for the special case: f(u)=u
p
, p>1. 相似文献
17.
Monotonicity of solutions and blow-up for
semilinear parabolic equations with nonlinear memory 总被引:2,自引:0,他引:2
We show the existence of monotone in time solutions for
a semilinear parabolic equation with memory. The blow-up rate
estimate of the solution is known to be a consequence of the
monotonicity property. 相似文献
18.
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
19.
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
20.
Fernando Quirós Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(2):357-362
We consider the heat equation in the half-line with
Dirichlet boundary data which blow up in finite time. Though the
blow-up set may be any interval [0,a],
depending on the Dirichlet data, we prove that the
effective
blow-up set, that is, the set of points
where the solution behaves like u(0,t), consists always only of the
origin.
As an application of our results we consider a system of two heat
equations with a nontrivial nonlinear flux coupling at the
boundary. We show that by prescribing the non-linearities the two
components may have different blow-up sets. However, the effective
blow-up sets do not depend on the coupling and coincide with the
origin for both components. 相似文献