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41.
In this paper we are interested in the semilinear elliptic equations of the type u=u(,u), on bounded smooth domain of R
n
. We also treat existence of positive solution of u=p(x)f(u), which explodes near the boundary of (called large solutions). Our approach is based on potential theory. 相似文献
42.
Hatem Samaali Fehmi Najar Slim Choura Ali H. Nayfeh Mohamed Masmoudi 《Nonlinear dynamics》2011,63(4):719-734
In this paper, we propose the design of an ohmic contact RF microswitch with low voltage actuation, where the upper and lower
microplates are displaceable. We develop a mathematical model for the RF microswitch made up of two electrostatically actuated
microplates; each microplate is attached to the end of a microcantilever. We assume that the microbeams are flexible and that
the microplates are rigid. The electrostatic force applied between the two microplates is a nonlinear function of the displacements
and applied voltage. We formulate and solve the static and eigenvalue problems associated with the proposed microsystem. We
also examine the dynamic behavior of the microswitch by calculating the limit-cycle solutions. We discretize the equations
of motion by considering the first few dominant modes in the microsystem dynamics. We show that only two modes are sufficient
to accurately simulate the response of the microsystem under DC and harmonic AC voltages. We demonstrate that the resulting
static pull-in voltage and switching time are reduced by 30 and 45%, respectively, as compared to those of a single microbeam-microplate
RF-microswitch. Finally, we investigate the global stability of the microswitch using different excitation conditions. 相似文献
43.
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45.
We prove existence and uniqueness of solutions to the Klein–Gordon–Zakharov system in the energy space H 1×L 2 on some time interval which is uniform with respect to two large parameters c and α. These two parameters correspond to the plasma frequency and the sound speed. In the simultaneous high-frequency and subsonic limit, we recover the nonlinear Schrödinger system at the limit. We are also able to say more when we take the limits separately. 相似文献
46.
47.
In this paper we study the convergence of weak solutions of the Navier Stokes equations with a large Coriolis term as the Rossby and Ekman numbers go to zero, and in particular the so called Ekman boundary layers, and justify some classical expansions in geophysical fluid dynamics (see [14], chapter 4). 相似文献
48.
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size \({\varepsilon}\) separated by distances \({d_{\varepsilon}}\) and the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit of \({\frac{d_{\varepsilon}}\varepsilon}\) when \({\varepsilon}\) goes to zero. If \({\frac{d_{\varepsilon}}\varepsilon \to \infty}\), then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary, \({\frac{d_{\varepsilon}}\varepsilon \to 0}\), then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit of \({\frac{d_{\varepsilon}}{\varepsilon^{2+\frac1\gamma}}}\) where \({\gamma \in (0,\infty]}\) is related to the geometry of the lateral boundaries of the obstacles. If \({\frac{d_{\varepsilon}}{\varepsilon^{2+\frac1\gamma}} \to \infty}\), then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal to \({\varepsilon^{3}}\) for balls. 相似文献
49.
50.
We deal with consistent first order non-relativistic corrections (i.e. in the small parameter , where c is the speed of light) of the Dirac–Maxwell system. We discuss a selfconsistent modeling of the Pauli equation as the O(ɛ) approximation of the Dirac equation. We suggest a coupling to the “magnetostatic”O(ɛ) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential. We sketch
the semiclassical/nonrelativistic limits of this model.
(Received 22 May 2000) 相似文献