On the Cauchy Problem for the Full Von Kk Armm an System
نویسنده
چکیده
We consider here the Cauchy problem for the full system of dynamic Von KK armm an equations, which is a model for the vibrations of a nonlinear elastic plate. We prove global existence and uniqueness of nite energy solutions in the case of an innnite plate. We show then that our methods and results still hold for a rectangular plate which is simply supported or clamped at the boundary. Moreover we obtain continuous dependence on the initial data.
منابع مشابه
Computation of Homoclinic Orbits in Partial Differential Equations: An Application to Cylindrical Shell Buckling
This paper concerns numerical computation of localised solutions in partial diier-ential equations (PDEs) on unbounded domains. The application is to the von KK armm an{Donnell equations, a coupled system of elliptic equations describing the equilibrium of an axially compressed cylindrical shell. Earlier work suggests that axially-localised solutions are the physically prefered buckling modes. ...
متن کاملExplicit Exponential Decay Rates for Solutions of Von K Arm An's System of Thermoelastic Plates
{ We consider the von KK armm an system for a bounded smooth ther-moelastic plate clamped on its boundary. We prove explicit exponential decay rates showing that the energy of solutions corresponding to initial data of energy equal to R decays as t ! 1 like exp (?!t=(1 + R 2)) for some universal positive constant !. A energia total E(t) decai como exp (?!t=(1 + R 2)) quando t vai para +1 sendo ...
متن کاملComputation of Localized Post Buckling in Long Axially-Compressed Cylindrical Shells
Buckling is investigated of a long thin cylindrical shell under longitudinal compression as modelled by the von KK armm an{Donnell equations. Evidence is reviewed for the buckling being localised to some portion of the axial length. In accordance with this observed behaviour the equations are rst approximated circumferentially by a Galerkin procedure, whereupon cross-symmetric homoclinic soluti...
متن کامل$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...
متن کاملBoundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linea...
متن کامل