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An asymptotically optimal model for isotropic heterogeneous linearly elastic plates

Ferdinando Auricchio, Carlo Lovadina, Alexandre L. Madureira (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with 5/6 as shear correction...

An elastic membrane with an attached non-linear thermoelastic rod

Werner Horn, Jan Sokołowski (2002)

International Journal of Applied Mathematics and Computer Science

We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence...

An elliptic equation with no monotonicity condition on the nonlinearity

Gregory S. Spradlin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...

An Elliptic Neumann Problem with Subcritical Nonlinearity

Jan Chabrowski, Kyril Tintarev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.

An elliptic semilinear equation with source term involving boundary measures: the subcritical case.

Marie Françoise Bidaut-Véron, Laurent Vivier (2000)

Revista Matemática Iberoamericana

We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2),⎧   Δu + uq = 0,   in Ω⎨⎩   u = μ,      on ∂Ωwhere 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted Marcinkiewicz spaces.

An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes

Sergey Grosman (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in a discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both, the perturbation parameters of the problem and the anisotropy of the mesh. The equilibrated residual method has been shown to provide one...

Currently displaying 521 – 540 of 5493