共查询到20条相似文献,搜索用时 31 毫秒
1.
In this work we study the blow up phenomena for some scalar delay differential equations. In particular, we make connection
with the blow up of ordinary differential equations that are related to the delay differential equations.
The first author is supported by a Grant from TWAS under contract No: 03-030 RG/MATHS/AF/AC.
The second author is supported by a grant from the Lebanese National Council for Scientific Research. 相似文献
2.
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
3.
Thierry Cazenave Flávio Dickstein Fred B. Weissler 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this paper, we prove sharp blow up and global existence results for a heat equation with nonlinear memory. It turns out that the Fujita critical exponent is not the one which would be predicted from the scaling properties of the equation. 相似文献
4.
Zhilei Liang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3507-3512
The present paper is concerned with the blow up rate of a solution to the following Cauchy problem
5.
Kai-Seng Chou Shi-Zhong Du Gao-Feng Zheng 《Calculus of Variations and Partial Differential Equations》2007,30(2):251-275
The global, weak solutions for the semilinear problem (1) introduced in Ni-Sacks-Tavantzis (J. Differ. Eq. 54, 97–120 (1984)) are studied. Estimates on the Hausdorff dimension of their singular sets are found. As an application, it
is shown that these solutions must blow up in finite time and become regular eventually when the nonlinearity is supercritical
and the domain is convex. 相似文献
6.
In this paper we study a simple non-local semilinear parabolic equation in a bounded domain with Neumann boundary conditions. We obtain a global existence result for initial data whose L∞-norm is less than a constant depending explicitly on the geometry of the domain. A natural energy is associated to the equation and we establish a relationship between the finite-time blow up of solutions and the negativity of their energy. The proof of this result is based on a Gamma-convergence technique. 相似文献
7.
Mauricio Bogoya 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):143-150
We analyze boundary value problems prescribing Dirichlet or Neumann boundary conditions for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation in a bounded smooth domain Ω∈RN with N≥1. First, we prove existence and uniqueness of solutions and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions. 相似文献
8.
We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which is assumed to be only measurable either in the time or the spatial variable. As functions of the other variables the coefficients have small bounded mean oscillation (BMO) semi-norms. The lower-order coefficients are allowed to blow up near the boundary with a certain optimal growth condition. As a corollary, we also obtain the corresponding results for elliptic equations. 相似文献
9.
Bashir Ahmad Ahmed Alsaedi Mokhtar Kirane 《Mathematical Methods in the Applied Sciences》2016,39(2):236-244
In this article, we prove the local existence of a unique solution to a nonlocal in time and space evolution equation with a time nonlocal nonlinearity of exponential growth. Moreover, under some suitable conditions on the initial data, it is shown that local solutions experience blow‐up. The time profile of the blowing‐up solutions is also presented. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
10.
We prove global existence and uniqueness of solutions of some important nonlinea lattices which include the Fermi-Pasta-Ularn (FPU) lattice. Our result shows (on a particular example) that the FPU lattice with high nonlinearity and its continuum limit display drastically different behaviour with respect to blow up phenomenon 相似文献
11.
12.
In this paper we study local existence, uniqueness, and continuous dependence of an abstract integrodifferential equation. We also present a result on unique continuation and a blow‐up alternative for mild solutions of the integrodifferential equation. Finally, we apply our results to an interesting strongly damped plate equation with memory. 相似文献
13.
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
14.
We establish the local well-posedness for the generalized Camassa–Holm equation. We also prove that the equation has smooth solutions that blow up in finite time. 相似文献
15.
In this paper a localized porous medium equation ut=ur(Δu+af(u(x0,t))) is considered. It is shown that under certain conditions solutions of the above equation blow up in finite time for large a or large initial data while there exist global positive solutions to the above equation for small a or small initial data. Moreover, it is also shown that all global positive solutions of the above equation are uniformly bounded, and this differs from that of a porous medium equation with a local source. 相似文献
16.
In the paper, we first use the energy method to establish the local well-posedness as well as blow-up criteria for the Cauchy problem on the two-component Euler–Poincaré equations in multi-dimensional space. In the case of dimensions 2 and 3, we show that for a large class of smooth initial data with some concentration property, the corresponding solutions blow up in finite time by using Constantin–Escher Lemma and Littlewood–Paley decomposition theory. Then for the one-component case, a more precise blow-up estimate and a global existence result are also established by using similar methods. Next, we investigate the zero density limit and the zero dispersion limit. At the end, we also briefly demonstrate a Liouville type theorem for the stationary weak solution. 相似文献
17.
We prove the uniform Hölder continuity of solutions for two classes of singularly perturbed parabolic systems. These systems arise in Bose-Einstein condensates and in competing models in population dynamics. The proof relies upon the blow up technique and the monotonicity formulas by Almgren and Alt, Caffarelli, and Friedman. 相似文献
18.
A blow up result for a fractionally damped wave equation 总被引:3,自引:0,他引:3
In this paper we prove a blow up result for solutions of the wave equation with damping of fractional order and in presence
of a polynomial source. This result improves a previous result in [5]. There we showed that the classical energy is unbounded
provided that the initial data are large enough. 相似文献
19.
In this paper, blow‐up property to a system of nonlinear stochastic PDEs driven by two‐dimensional Brownian motions is investigated. The lower and upper bounds for blow‐up times are obtained. When the system parameters satisfy certain conditions, the explicit solutions of a related system of random PDEs are deduced, which allows us to use Yor's formula to obtain the distribution functions of several blow‐up times. Particularly, the impact of noises on the life span of solutions is studied as the system parameters satisfy different conditions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
20.
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