We address three related problems in the theory of elasticity, formulated framework double forms: Saint-Venant compatibility condition, existence and uniqueness solutions for equations arising incompatible stress potentials. The scope this work is manifolds with boundary arbitrary dimension, having constant sectional curvature. central analytical machinery regular ellipticity a boundary-value p...

A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy.

We study the local exponential stabilization of the 3D NavierStokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equation be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In orde...

Paraxial light in a Cole-Cole nonlocal medium: integrable regimes and singularities. ABSTRACT Nonlocal nonlinear Schrödinger-type equation is derived as a model to describe paraxial light propagation in nonlinear media with different 'degrees' of nonlocality. High frequency limit of this equation is studied under specific assumptions of Cole-Cole dispersion law and a slow dependence along propa...

A general scheme for analyzing reductions of Whitham hierarchies is presented. It is based on a method for determining the S-function by means of a system of first order partial differential equations. Compatibility systems of differential equations characterizing both reductions and hodograph solutions of Whitham hierarchies are obtained. The method is illustrated by exhibiting solutions of in...

The general theory of compatibility conditions for the differentiability of solutions to initial-boundary value problems is well known. This paper introduces the application of that theory to numerical solutions of partial differential equations and its ramifications on the performance of high-order methods. Explicit application of boundary conditions (BCs) that are independent of the initial c...

We prove that the special value conjecture for Zeta function ζ(X , s) of a proper, regular arithmetic scheme X we formulated in [8][Conj. 5.12] is compatible with functional equation provided factor C(X n) were not able to compute loc. cit. has simple explicit form suggested [9].

The present work involves numerical simulation of a steady, incompressible forcedconvection fluid flow through a matrix of porous media between two parallel plates at constanttemperature. A Darcy model for the momentum equation was employed. The mathematical model forenergy transport was based on single phase equation model which assumes local thermal equilibriumbetween fluid and solid phases. ...