Search results for "Partial"

Partial differential equations and quasiregular mappings

1992

Singular distributed parameter systems

1993

The paper deals with the distributed parameter systems described by coupled partial differential equations with singular matrix coefficients. Initial-boundary-value problems are considered in the light of both singular 1d systems theory and the Fourier approach to distributed parameter systems. The method presented in this paper gives the possibility of determining acceptable initial-boundary conditions. An illustrative example is given.

Boundary-layer effects in wedges of piezoelectric laminates

2005

An approach to investigate boundary-layer effects in wedges of piezoelectric laminated structures is presented with the aim of ascertaining the electromechanical response characteristics. The wedge layer behavior is described in terms of generalized stress functions, which lead to a model consisting of a set of three coupled partial differential equations. The strength of the solution singularity is determined by solving the eigenvalue problem associated with the resolving system. The solution of the model is obtained by an eigenfunction expansion method coupled with a boundary collocation technique. Correspondingly, the singularity amplitude is assessed by introducing and calculating the g…

SPECIAL SPLINES OF HYPERBOLIC TYPE FOR THE SOLUTIONS OF HEAT AND MASS TRANSFER 3-D PROBLEMS IN POROUS MULTI-LAYERED AXIAL SYMMETRY DOMAIN

2017

In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the cons…

Mauro Picone, Sandro Faedo, and the numerical solution of partial differential equations in Italy (1928-1953)

2013

In this paper we revisit the pioneering work on the numerical analysis of partial differential equations (PDEs) by two Italian mathematicians, Mauro Picone (1885-1977) and Sandro Faedo (1913-2001). We argue that while the development of constructive methods for the solution of PDEs was central to Picone's vision of applied mathematics, his own work in this area had relatively little direct influence on the emerging field of modern numerical analysis. We contrast this with Picone's influence through his students and collaborators, in particular on the work of Faedo which, while not the result of immediate applied concerns, turned out to be of lasting importance for the numerical analysis of …

Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration

2016

A positive solution of a homogeneous Dirichlet boundary value problem or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of its level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. We show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric, in the sense that is contained in and contains two concentric balls $${B_{{r_e}}}$$ and $${B_{{r_i}}}$$ , with the difference r e -r i (linearly) controlled by a suitable norm of the deviation…

On the Extremals of a Functional on the Plane

2004

Strain gradient elasticity within the symmetric BEM formulation

2014

The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 1/ r 4 . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a resear…

Multiplicity results for Sturm-Liouville boundary value problems

2009

Multiplicity results for Sturm-Liouville boundary value problems are obtained. Proofs are based on variational methods.

Superharmonic functions are locally renormalized solutions

2011

Abstract We show that different notions of solutions to measure data problems involving p-Laplace type operators and nonnegative source measures are locally essentially equivalent. As an application we characterize singular solutions of multidimensional Riccati type partial differential equations.