共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
Lei Zhu & Faxing Wang 《偏微分方程(英文版)》2015,28(1):23-29
In this paper, we give a new blowup criteria of strong solutions to the Oldroyd model for ideal viscoelastic flow. 相似文献
3.
The paper studies the blowup of solutions to the initial boundary value problem for the “bad” Boussinesq-type equation utt−uxx−buxxxx=σ(u)xx, where b>0 is a real number and σ(s) is a given nonlinear function. By virtue of the energy method and the Fourier transform method, respectively, it proves that under certain assumptions on σ(s) and initial data, the generalized solutions of the above-mentioned problem blow up in finite time. And a few examples are shown, especially for the “bad” Boussinesq equation, two examples of blowup of solutions are obtained numerically. 相似文献
4.
The paper studies the existence and uniqueness of local solutions and the blowup of solutions to the initial boundary value problem for improved Boussinesq type equation utt−uxx−uxxtt=σ(u)xx. By a Galerkin approximation scheme combined with the continuation of solutions step by step and the Fourier transform method, it proves that under rather mild conditions on initial data, the above-mentioned problem admits a unique generalized solution u∈W2,∞([0,T];H2(0,1)) as long as . In particular, when σ(s)=asp, where a≠0 is a real number and p>1 is an integer, specially a<0 if p is an odd number, the solution blows up in finite time. Moreover, two examples of blowup are obtained numerically. 相似文献
5.
6.
Kwang Ik Kim 《Journal of Mathematical Analysis and Applications》2004,293(2):663-676
Blowup estimates for solutions of a parabolic system, which arises in a cooperating three-species food chain model, with homogeneous Dirichlet boundary conditions are investigated. The upper bound of blowup rate for any N and the lower bound of blowup rate for N=1 are obtained. 相似文献
7.
8.
We study asymptotics as t → ∞ of solutions to a linear, parabolic system of equations with time‐dependent coefficients in Ω × (0, ∞), where Ω is a bounded domain. On ? Ω × (0, ∞) we prescribe the homogeneous Dirichlet boundary condition. For large values of t, the coefficients in the elliptic part are close to time‐independent coefficients in an integral sense which is described by a certain function κ (t). This includes in particular situations when the coefficients may take different values on different parts of Ω and the boundaries between them can move with t but stabilize as t → ∞. The main result is an asymptotic representation of solutions for large t. As a corollary, it is proved that if κ ∈ L1(0, ∞), then the solution behaves asymptotically as the solution to a parabolic system with time‐independent coefficients (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
The paper studies the existence and non-existence of global weak solutions to the Cauchy problem for the multi-dimensional Boussinesq type equation utt−Δu+Δ2u=Δσ(u). It proves that the Cauchy problem admits a global weak solution under the assumptions that σ∈C(R), σ(s) is of polynomial growth order, say p (>1), either , s∈R, where β>0 is a constant, or the initial data belong to a potential well. And the weak solution is regularized and the strong solution is unique when the space dimension N=1. In contrast, any weak solution of the Cauchy problem blows up in finite time under certain conditions. And two examples are shown. 相似文献
10.
Mingtao Chen 《Nonlinear Analysis: Real World Applications》2012,13(2):850-859
We prove that the maximum norm of velocity gradients controls the possible breakdown of smooth (strong) solutions for the 3-dimensional viscous, compressible micropolar fluids. More precisely, if a solution of the system is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without the bound of the velocity gradients as the critical time approaches. Our result is a generalization of Huang et al. (2011) [13] from viscous barotropic flows to the viscous, compressible micropolar fluids. In addition, initial vacuum states are also allowed in our result. 相似文献
11.
The Blowup Mechanism of Small Data Solutions for the Quasilinear Wave Equations in Three Space Dimensions 总被引:1,自引:0,他引:1
Hui Cheng Yin 《数学学报(英文版)》2001,17(1):35-76
For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and Hörmander. As an application of our result, we show that the solution of three-dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac. 相似文献
12.
13.
Zhilei Liang 《Journal of Mathematical Analysis and Applications》2010,370(2):506-3825
The blowup phenomena of solutions of the compressible Euler equations is investigated. The approach is to construct the special solutions and use phase plane analysis. In particular, the special explicit solutions with velocity of the form c(t)x are constructed to show the blowup and expanding properties. 相似文献
14.
Zhijian Yang 《Journal of Mathematical Analysis and Applications》2004,300(1):218-243
The paper studies the existence and non-existence of global weak solutions to the Cauchy problem for a class of quasi-linear wave equations with nonlinear damping and source terms. It proves that when α?max{m,p}, where m+1, α+1 and p+1 are, respectively, the growth orders of the nonlinear strain terms, the nonlinear damping term and the source term, under rather mild conditions on initial data, the Cauchy problem admits a global weak solution. Especially in the case of space dimension N=1, the weak solutions are regularized and so generalized and classical solution both prove to be unique. On the other hand, if 0?α<1, and the initial energy is negative, then under certain opposite conditions, any weak solution of the Cauchy problem blows up in finite time. And an example is shown. 相似文献
15.
在一定的结构性条件下,证明了如下形式的拟线性退化抛物方程 Cauchy问题解的稳定性. 相似文献
16.
T. A. Suslina 《Functional Analysis and Its Applications》2004,38(4):309-312
We study homogenization in the small period limit for a periodic parabolic Cauchy problem in d and prove that the solutions converge in L
2(d) to the solution of the homogenized problem for each t > 0. For the L2(d)-norm of the difference, we obtain an order-sharp estimate uniform with respect to the L
2(d)-norm of the initial value.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 86–90, 2004Original Russian Text Copyright © by T. A. SuslinaSupported by RFBR grant No. 02-01-00798. 相似文献
17.
Radu Miculescu Alexandru Mihail 《Proceedings of the American Mathematical Society》2008,136(2):587-592
It is known that Lipscomb's space can be imbedded in Hilbert's space . Let be the imbedded version of endowed with the -induced topology. We show how to construct as the attractor of an iterated function system containing an infinite number of affine transformations of . In this way we answer an open question of J.C. Perry.
18.
Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations
下载免费PDF全文
![点击此处可从《偏微分方程(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space. 相似文献
19.
V. B. Levenshtam 《Mathematical Notes》1999,65(4):470-478
An algorithm for constructing the higher approximations of the averaging method for quasilinear parabolic equations with fast
oscillating coefficients is suggested and justified.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 562–572, April, 1999. 相似文献
20.
Andrew Hassell 《Transactions of the American Mathematical Society》2000,352(8):3799-3820
Let be a generalized body Schrödinger operator with very short range potentials. Using Melrose's scattering calculus, it is shown that the free channel `geometric' scattering matrix, defined via asymptotic expansions of generalized eigenfunctions of , coincides (up to normalization) with the free channel `analytic' scattering matrix defined via wave operators. Along the way, it is shown that the free channel generalized eigenfunctions of Herbst-Skibsted and Jensen-Kitada coincide with the plane waves constructed by Hassell and Vasy and if the potentials are very short range.