共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Yu. M. Mamedov 《Journal of Mathematical Sciences》1993,65(5):1855-1860
The construction of potential theory for two-dimensional quasistatic problems of uncoupled thermoelasticity is carried out by considering the full system of differential equations of the problem as a nonselfadjoint differential operator. Green's second formula for this operator is interpreted as a duality theorem that differs from Mizel's duality theorem. In the case of a homogeneous isotropic medium we construct new integral equations for the basic initial-boundary value problems.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 48–52. 相似文献
3.
4.
5.
E. V. Altukhov 《Journal of Mathematical Sciences》1997,84(6):1469-1472
We obtain the homogeneous thermal solutions due to a temperature field for the three-dimensional thermoelastic problem for
isotropic plates on whose plane faces homogeneous thermal and mixed mechanical conditions of flat face and diaphragm type
are prescribed. This makes it possible to reduce the thermoelastic boundary-value problem to the corresponding elasticity
problem.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika. No. 25, 1995, pp. 3–8. 相似文献
6.
The aim of this investigation is to determine the wave field inside a part of a conic domain filled with an acoustic medium
subjected to the action of a nonstationary pressure. The method of solution is based on the discretization of the problem
with respect to time by replacing the second derivative by a difference scheme and using new integral transformations with
respect to other variables. A recurrent solution of the problem is obtained, and the calculation of a wave field for different
geometric parameters of the domain is performed. 相似文献
7.
8.
Jesus Garcia Azorero Andrea Malchiodi Luigi Montoro Ireneo Peral 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper [J. Garcia Azorero, A. Malchiodi, L. Montoro, I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Existence results, Arch. Ration. Mech. Anal., in press]. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in [J. Garcia Azorero, A. Malchiodi, L. Montoro, I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Existence results, Arch. Ration. Mech. Anal., in press]. 相似文献
9.
P. Ya. Malits 《Journal of Mathematical Sciences》1993,65(2):1564-1569
A method of solving paired integral equations that appear in considerations of mixed problems of elasticity and thermoelasticity theory is given, with the help of generalized integral Weber transforms. The paired equations are reduced to an integral Fredholm equation of the second kind on the semiaxis, which have a discontinuous kernel, or to Fredholm equations of the second kind on a finite interval and infinite systems of linear algebraic equations, which are normal in the sense of Poincare-Koch. As an example, contact problems for an inhomogeneous fiber with a cavity are considered. If the fiber is bonded with the elastic half-space, then a second appproach is realized, which is based on a reduction to an equation with a self-adjoint operator, for which some method of sequential iteractions and the Bubnov-Galerkin method are justified.Translated from Dinamicheskie Sistemy, No. 7, pp. 95–102, 1988. 相似文献
10.
Jiangang Cheng 《Journal of Mathematical Analysis and Applications》2006,313(1):322-341
This paper is concerned with the exact number of positive solutions for the boundary value problem ′(|y′|p−2y′)+λf(y)=0 and y(−1)=y(1)=0, where p>1 and λ>0 is a positive parameter. We consider the case in which both f(u) and g(u)=(p−1)f(u)−uf′(u) change sign exactly once from negative to positive on (0,∞). 相似文献
11.
R.S. Gevorgyan 《Journal of Applied Mathematics and Mechanics》2008,72(1):87-91
The asymptotic method of solving boundary-value problems of the theory of elasticity for anisotropic strips and plates is used to solve coupled dynamic problems of thermoelasticity for plates, on the faces of which the values of the temperature function and the values of the components of the displacement vector or the conditions of the mixed problem of the theory of elasticity are specified. Recurrence formulae are derived for determining the components of the displacement vector, the stress tensor and for the temperature field variation function of the plate. 相似文献
12.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(1):226-238
The velocity field and the shear stress corresponding to the motion of a generalized Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent shear stress are established by means of the Laplace and finite Hankel transforms. The exact solutions, written under series form, can be easily specialized to give the similar solutions for generalized Maxwell and generalized second grade fluids as well as for ordinary Oldroyd-B, Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid are shown by graphical illustrations. 相似文献
13.
Jiangang Cheng 《Journal of Mathematical Analysis and Applications》2003,280(2):197-208
This paper is concerned with the boundary value problems y″+λ(yp−yq)=0 and y(−1)=y(1)=0, where p>q>−1 and λ>0 is a positive parameter. We discuss the existence of positive solutions and give a complete study. 相似文献
14.
The mathematical theory of elasticity for planar pentagonal quasicrystals is developed and some analytic solutions for a class
of mixed boundary-value problems (corresponding to a Griffith crack) of the theory are offered. An alternate procedure and
a direct integral approach are proposed. Some analytical solutions are constructed and the stress and displacement fields
of a Griffith crack in the quasicrystals are determined. A basis for further studying the mechanical behavior of the material
related to planar defects is provided.
Project supported by the Foundation of State Education Commission of China for Doctorate Station. 相似文献
15.
In this paper we study the existence of positive solutions of the equation
(φ(x′))′+a(t)f(x(t))=0, 相似文献
16.
《Journal of Applied Mathematics and Mechanics》2002,66(1):99-105
The sine-Gordon equation with dissipation and a variable coefficient on the non-linear term is considered. This equation describes waves in an energetically open system with an external field acting on it which varies monotonically with time. Scale transformations, matched with the external field and the dissipation, are introduced which reduce the generalized equation to the standard equation. It is shown that processes for controlling the oscillations and waves exist for which the equation is transformed to a form with constant coefficients and an effective dissipation which vanishes or is either positive (damping of the oscillations) or negative (their amplification). Waves, which propagate with a constant, decaying or increasing amplitude and variable frequency and velocity correspond to them. 相似文献
17.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(7):2788-2795
Unsteady flow of an incompressible generalized Maxwell fluid between two coaxial circular cylinders is studied by means of the Laplace and finite Hankel transforms. The motion of the fluid is produced by the rotation of cylinders around their common axis. The solutions that have been obtained, written in integral and series form in terms of the generalized Ga,b,c(·, t)-functions, are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. They satisfy all imposed initial and boundary conditions and for λ → 0 reduce to the solutions corresponding to the Newtonian fluids performing the same solution. Furthermore, the corresponding solutions for ordinary Maxwell fluids are also obtained for β = 1. Finally, in order to reveal some relevant physical aspects of the obtained results, the diagrams of the velocity field ω(r, t) have been depicted against r and t for different values of the material and fractional parameters. 相似文献
18.
Marco Ghimenti Anna Maria Micheletti Angela Pistoia 《Journal of Fixed Point Theory and Applications》2013,14(2):503-525
Let (M, g) and \({(K, \kappa)}\) be two Riemannian manifolds of dimensions m and k, respectively. Let \({\omega \in C^{2} (N), \omega > 0}\) . The warped product \({M \times_\omega K}\) is the (m + k)-dimensional product manifold \({M \times K}\) furnished with metric \({g + \omega^{2} \kappa}\) . We prove that the supercritical problem $$- \Delta_{g + \omega^{2} \kappa} u + hu = u^{\frac{m+2}{m-2} \pm \varepsilon} ,\quad u > 0,\quad {\rm in}\,\, (M \times_{\omega} K, g + \omega^{2} \kappa)$$ has a solution concentrated along a k-dimensional minimal submanifold \({\Gamma}\) of \({M \times_{\omega } N}\) as the real parameter \({\varepsilon}\) goes to zero, provided the function h and the sectional curvatures along \({\Gamma}\) satisfy a suitable condition. 相似文献
19.
In the present work, the exact analytic solutions for some oscillating flows of a generalized second grade fluid are investigated using Fourier sine and Laplace transforms. A more appropriate model is presented for fluid material between viscous and elastic to introduce the fractional calculus approach into the constitutive relationship. This paper employs the fractional calculus approach to study second grade fluid flows. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method has been used. Similar solutions for second grade fluid appear as the limiting cases of our solutions. The influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn. 相似文献
20.
In this paper, the existence and multiplicity results of solutions are obtained for the discrete nonlinear two point boundary value problem (BVP) ; u(0)=0=Δu(T), where T is a positive integer, Z(1,T)={1,2,…,T}, Δ is the forward difference operator defined by Δu(k)=u(k+1)-u(k) and f:Z(1,T)×R→R is continuous, λ∈R+ is a parameter. By using the critical point theory and Morse theory, we obtain that the above (BVP) has solutions for λ being in some different intervals. 相似文献