Uniqueness of solutions for an elliptic equation modeling MEMS
نویسنده
چکیده
This equation has been proposed as a model for a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 below a rigid ground plate located at height z = 1. See [10, 11]. A voltage – directly proportional to the parameter λ – is applied, and the membrane deflects towards the ground plate and a snap-through may occur when it exceeds a certain critical value λ∗, the pull-in voltage. In [9] a fine ODE analysis of the radially symmetric case with a profile f ≡ 1 on a ball B, yields the following bifurcation diagram that describes the L∞-norm of the solutions u – which in this case necessarily coincides with u(0) – in terms of the corresponding voltage λ.
منابع مشابه
On uniqueness in the general inverse transmisson problem
In this paper we demonstrate uniqueness of a transparent obstacle, of coefficients of rather general boundary transmission condition, and of potential coefficient inside obstacle from partial Dirichlet-to Neumann map or from complete scattering data at fixed frequency. The proposed transmission problem includes in particular isotropic elliptic equation with discontinuous conductivity coefficien...
متن کاملNonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution
This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملExistence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کاملOn existence and uniqueness of solutions of a nonlinear Volterra-Fredholm integral equation
In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we give an example to illustrate the applications of our results.
متن کامل