共查询到20条相似文献,搜索用时 15 毫秒
1.
Irena Pawow Wojciech M. Zajaczkowski 《Mathematical Methods in the Applied Sciences》2005,28(4):407-442
This paper is concerned with the unique global solvability of a three‐dimensional (3‐D) non‐linear thermoelasticity system arising from the study of shape memory materials. The system consists of the coupled evolutionary problems of viscoelasticity with non‐convex elastic energy and non‐linear heat conduction with mechanical dissipation. The present paper extends the previous 2‐D existence result of the authors Reference [1] to 3‐D case. This goal is achieved by means of the Leray–Schauder fixed point theorem using technique based on energy arguments and DeGiorgi method. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Salim A. Messaoudi Belkacem Said‐Houari 《Mathematical Methods in the Applied Sciences》2005,28(2):205-232
In this paper, we consider a one‐dimensional non‐linear system of thermoelasticity with second sound. We establish an exponential decay result for solutions with small ‘enough’ initial data. This work extends the result of Racke (Math. Methods Appl. Sci. 2002; 25 :409–441) to a more general situation. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
4.
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
5.
Larbi Berrahmoune 《Mathematical Methods in the Applied Sciences》2004,27(12):1385-1398
We consider an initial and boundary value problem for a homogenous string subject to an internal pointwise control. The solution resulting from a non‐linear feedback is studied. We give various explicit decay estimates depending on the control position and the feedback non‐linearity. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
6.
《Mathematical Methods in the Applied Sciences》2018,41(7):2811-2826
In this work, the modified Green function technique for the exterior Dirichlet problem in linear thermoelasticity is presented. Expressing the solution of the problem as a double‐layer potential of an unknown density, we form the associated boundary integral equation that describes the problem. Exploiting that the discrete spectrum of the irregular values of the associated integral equation is identified with the spectrum of eigenvalues of the corresponding interior homogeneous Neumann problem for the transverse part of the elastic displacement field, we introduce a modification of the fundamental solution of the elastic field. We establish the sufficient conditions that the coefficients of the modification must satisfy to overcome the problem of nonuniqueness for the thermoelastic problem. 相似文献
7.
To Fu Ma 《Mathematical Methods in the Applied Sciences》2001,24(8):583-594
In this paper, we study the equation under non‐linear boundary conditions which model the vibrations of a beam clamped at x=0 and supported by a non‐linear bearing at x=L. By adding only one damping mechanism at x=L, we prove the existence of a global solution and exponential decay of the energy. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
8.
Toshihiro Kobayashi 《Mathematical Methods in the Applied Sciences》2004,27(1):79-89
This paper is concerned with global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system has an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by linear boundary control. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
9.
J. Giroire T. Ha‐Duong V. Moumas 《Mathematical Methods in the Applied Sciences》2005,28(13):1527-1552
This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
10.
Xu Zhang 《Mathematical Methods in the Applied Sciences》1999,22(3):259-265
In this paper, by means of the method of implicit discretization in time, we obtain the existence of weak solution for a class of non‐linear parabolic boundary value problem with equivalued surface. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
11.
Toshihiro Kobayashi Tetsuzo Sakamoto 《Mathematical Methods in the Applied Sciences》2007,30(10):1209-1221
This paper is concerned with adaptive global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system may have an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The adaptive stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by adaptive boundary control. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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In this paper, we consider an inexact Newton method applied to a second order non‐linear problem with higher order non‐linearities. We provide conditions under which the method has a mesh‐independent rate of convergence. To do this, we are required, first, to set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial non‐linear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory. Published in 2005 by John Wiley & Sons, Ltd. 相似文献
13.
We prove that the quasilinear initial value problem (1) has a unique, local in time, C1 solution, if the matrices Ai are diagonalizable and commute with each other. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
Paula Budu 《Mathematical Methods in the Applied Sciences》2004,27(4):457-475
The thermal convection in a layer of a third grade fluid is investigated, with viscosity being a general function of temperature. We develop a non‐linear stability analysis and prove that unconditional non‐linear stability criterion is achieved using a natural energy approach. This shows that, in some sense, the equations for a fluid of third grade are preferable to those for a fluid of second grade or a dipolar fluid. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
W. Malfliet 《Mathematical Methods in the Applied Sciences》2005,28(17):2031-2035
The tanh (or hyperbolic tangent) method is a powerful technique to look for travelling waves when dealing with one‐dimensional non‐linear wave and evolution equations. In particular, this method is well suited for those problems where dispersion, convection and reaction–diffusion play an important role. To show the strength of this method we study a coupled set (the so‐called Boussinesq equations) which arises in the theory of non‐linear dispersive water waves. As a result, a solitary wave profile is found which generalizes an earlier result, the famous Korteweg‐de Vries solitary wave solution. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
16.
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
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In this paper the degenerate parabolic system ut=u(uxx+av). vt=v(vxx+bu) with Dirichlet boundary condition is studied. For , the global existence and the asymptotic behaviour (α1=α2) of solution are analysed. For , the blow‐up time, blow‐up rate and blow‐up set of blow‐up solution are estimated and the asymptotic behaviour of solution near the blow‐up time is discussed by using the ‘energy’ method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
18.
Salim A. Messaoudi 《Mathematical Methods in the Applied Sciences》2005,28(15):1819-1828
In this paper, we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on α, m, and p, we give precise decay rates for the solution. In particular, we show that for m=0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25 :795–814). Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
19.
《Mathematical Methods in the Applied Sciences》2018,41(10):3868-3884
We investigate in this paper a thermoelastic system where the oscillations are defined by the Timoshenko model and the heat conduction is given by Green and Naghdi theories. We introduce 2 new stability numbers κ1 , κ2, and we prove a general decay result, from which the exponential and polynomial decays are only special cases. 相似文献
20.
Marian Bie 《Mathematical Methods in the Applied Sciences》2005,28(9):1007-1030
The existence of global‐in‐time weak solutions to the Joule problem modelling heating or cooling in a current and heat conductive medium is proved via the Faedo–Galerkin method. The existence proof entails some a priori estimates that together with the monotonicity and compactness methods make up a main tool to prove the desired result. Under appropriate hypotheses on the data, it will be shown the boundedness in L∞(QT) of the absolute temperature of the medium and of the t‐derivative of this temperature, which is achieved by means of the Gagliardo–Nirenberg theorem, the Sobolev embedding theorem and the method of Stampacchia. The paper is some extension of our investigation initiated in (Math. Meth. Appl. Sci. 1998; 23 :1275–1291). This extension includes relaxing some assumptions in (Math. Meth. Appl. Sci. 1998; 23 :1275–1291) and employing some new methods to establish the result. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献