Existence of weak solutions in elasticity

Existence of weak solutions in elasticity

Weak Solutions in Elasticity of Dipolar Porous Materials

The theories of porous materials represent a material length scale and are quite sufficient for a large number of the solid mechanics applications. In the following, we restrict our attention to the behavior of the porous solids in which the matrix material is elastic and the interstices are voids of material. The intended applications of this theory are to the geological materials, like rocks ...

Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

Existence 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...

Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we develop such connections for the case of two spatial dimensions, and demonstrate that the continuum mechanical equations can be mapped into a corresponding geome...