共查询到20条相似文献，搜索用时 0 毫秒
1.
The initial and initial‐boundary value problems for the Kuramoto–Sivashinsky model of “fluid‐solid particles” media are considered. Existence, uniqueness and asymptotic behaviour of strong solutions are proved. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
J. Gawinecki 《Mathematical Methods in the Applied Sciences》2003,26(11):907-936
We consider some initial–boundary value problems for non‐linear equations of thermoviscoelasticity in the three‐dimensional case. Since, we are interested to prove global existence we consider spherically symmetric problem. We examine the Neumann conditions for the temperature and either the Neumann or the Dirichlet boundary conditions for the elasticity equations. Using the energy method, we are able to obtain some energy estimates in appropriate Sobolev spaces enough to prove existence for all time without any restrictions on data. Due to the spherical symmetricity the constants in the above estimates increase with time so the existence for all finite times is proved only. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
3.
J. Límaco H. R. Clark A. J. Feitosa 《Mathematical Methods in the Applied Sciences》2005,28(4):457-478
We investigate a initial‐boundary value problem for the nonlinear beam equation with variable coefficients on the action of a linear internal damping. We show the existence of a unique global weak solution and that the energy associated with this solution has a rate decay estimate. Besides, we prove the existence and uniqueness of non‐local strong solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
4.
Le Thi Phuong Ngoc Nguyen Thanh Long 《Mathematical Methods in the Applied Sciences》2014,37(4):464-487
This paper is devoted to the study of a system of nonlinear equations with nonlinear boundary conditions. First, on the basis of the Faedo–Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, the exponential decay property of the global solution via the construction of a suitable Lyapunov functional is presented. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
5.
Fengquan Li 《Mathematical Methods in the Applied Sciences》2004,27(10):1115-1124
In this paper, we discuss the existence and uniqueness of bounded weak solution for non‐linear parabolic boundary value problem with equivalued surface and correct the mistake in Zhang Xu (Math. Meth. Appl. Sci. 1999; 22 : 259). The approach is based on L∞ estimate of solution. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
6.
7.
Li Fushan~ 《Annals of Differential Equations》2007,23(3):273-279
In this paper,we consider the linearly viscoelastic equations for Koiter shells. Also,we prove the existence and uniqueness of the solution by Galerkin method. 相似文献
8.
Irena Pawłow Wojciech M. Zaja̧czkowski 《Mathematical Methods in the Applied Sciences》2009,32(17):2197-2242
In this paper we prove the existence and uniqueness of a global in time, regular solution to the Cahn–Hilliard system coupled with viscoelasticity. The system arises as a model, regularized by a viscous damping, of phase separation process in a binary deformable alloy quenched below a critical temperature. The key tools in the analysis are estimates of absorbing type with the property of exponentially time‐decreasing contribution of the initial data. Such estimates allow not only to prolong the solution step by step on the infinite time interval but also to conclude the existence of an absorbing set. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
9.
Let be a bounded domain in #x211D;n with a smooth boundary . In this work we study the existence of solutions for the following boundary value problem:
where M is a C1-function such that M() 0 > 0 for every 0 and f(y) = |y|y for 0. 相似文献
10.
In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
11.
This paper is concerned with the existence, nonexistence, uniqueness, and non‐uniqueness of solutions for a singular parabolic equation in one dimension case. For different cases of some constant m of the equation, we study the uniqueness of solutions for m > ? 1, the nonexistence of solutions for m ≤ ? p, and the existence and non‐uniqueness of solutions for ? p < m ≤ ? 1. The novelty of this paper lies in the study of nonexistence. Moreover, the other results of this paper extend some recent works. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
12.
We study a class of compressible non‐Newtonian fluids in one space dimension. We prove, by using iterative method, the global time existence and uniqueness of strong solutions provided that the initial data satisfy a compatibility condition and the initial density is small in its H1‐norm. The main difficulty is due to the strong nonlinearity of the system and the initial vacuum. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
Salim A. Messaoudi Belkacem Said Houari 《Mathematical Methods in the Applied Sciences》2004,27(14):1687-1696
In this paper we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. We prove, under suitable conditions on α,β,m,p and for negative initial energy, a global non‐existence theorem. This improves a result by Yang (Math. Meth. Appl. Sci. 2002; 25 :825–833), who requires that the initial energy be sufficiently negative and relates the global non‐existence of solutions to the size of Ω. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
14.
研究了一类非线性耦合双曲型方程组初边值问题,讨论了初边值条件以及非线性项中指数满足的条件,利用Galerkin方法和紧致性的结果,以及椭圆型方程解的正则性定理,经过严格的推导证明了该问题解的存在唯一性的若干结果. 相似文献
15.
In this paper we propose a model to study superfluidity by considering as state variables the order parameter, describing the concentration of the superfluid phase, the velocity of the superfluid and the absolute temperature. We assume that the order parameter satisfies a Ginzburg–Landau equation and that the velocity is decomposed as the sum of a normal and a superfluid component. The heat equation provides the evolution equation for the temperature. We prove that this model is consistent with the principles of thermodynamics. Well‐posedness of the resulting initial and boundary value problem is shown. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
16.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
where q>1, q1, >0, >0, 0,
is the Laplacian in
. 相似文献
17.
用Galerkin方法研究了Koiter壳动力学方程,得到了解的存在性与唯一性结果。 相似文献
18.
Eleni Bisognin Vanilde Bisognin Mauricio Sepúlveda Octavio Vera 《Journal of Computational and Applied Mathematics》2008,220(1-2):290-321
We consider the initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of Korteweg–de Vries (KdV)-type modelling strong interactions between internal solitary waves. Finite domains of wave propagation changing in time arise naturally in certain practical situations when the equations are used as a model for waves and a numerical scheme is needed. We prove a global existence and uniqueness for strong solutions for the coupled system of equations of KdV-type as well as the exponential decay of small solutions in asymptotically cylindrical domains. Finally, we present a numerical scheme based on semi-implicit finite differences and we give some examples to show the numerical effect of the moving boundaries for this kind of systems. 相似文献
19.
Chandi Bhandari Ronald H.W. Hoppe Rahul Kumar 《Numerical Methods for Partial Differential Equations》2019,35(4):1477-1496
We prove the existence and uniqueness of a solution of a C0 Interior Penalty Discontinuous Galerkin (C0 IPDG) method for the numerical solution of a fourth‐order total variation flow problem that has been developed in part I of the paper. The proof relies on a nonlinear version of the Lax‐Milgram Lemma. It requires to establish that the nonlinear operator associated with the C0 IPDG approximation is Lipschitz continuous and strongly monotone on bounded sets of the underlying finite element space. 相似文献
20.
P. Braz e Silva M. A. Rojas‐Medar E. J. Villamizar‐Roa 《Mathematical Methods in the Applied Sciences》2010,33(3):358-372
We show the existence of strong solutions for the nonhomogeneous Navier–Stokes equations in three‐dimensional domains with boundary uniformly of class C3. Under suitable assumptions, uniqueness is also proved. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献