Construction of Periodic Solutions of Nonlinear Wave equations in Higher Dimension.
Construction of Singular Solutions to the P-Harmonic Equation and its Limit Equation for P = ... .
Construction of Sobolev spaces of fractional order with sub-riemannian vector fields
Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.
Construction of the Leray-Schauder degree for elliptic operators in unbounded domains
Construction of the wave group for higher order elliptic boundary value problems
Construction solutions of PDE in parametric form.
Contact between elastic bodies. I. Continuous problems
Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed.
Contact geometry of hyperbolic equations of generic type.
Contact geometry of hyperbolic Monge-Ampére equations.
Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions
We study the geometry of multidimensional scalar order PDEs (i.e. PDEs with independent variables), viewed as hypersurfaces in the Lagrangian Grassmann bundle over a -dimensional contact manifold . We develop the theory of characteristics of in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of . After specializing such results to general Monge-Ampère equations (MAEs), we focus our attention to MAEs of...
Contact integrable extensions and differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
Contact problem of two elastic bodies. I
The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.
Contact problem of two elastic bodies. II
The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.
Contact problem of two elastic bodies. III
The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.
Contact problems with given time-dependent friction force in linear viscoelasticity
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