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Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation [PDF]

, 1968
G. Fichera [1] and other authors have investigated partial differential equations of the form [Eq. 1.1] in which the matrix (aij(x)) is required to be semidefinite. Equations of this type occur in the theory of random processes.
J. Franklin, E. Rodemich
semanticscholar   +3 more sources

Coefficient Identification in Elliptic Partial Differential Equation [PDF]

Large-Scale Scientific Computing, 2006
We consider the inverse problem for identification of the coefficient in an elliptic partial differential equation inside of the unit square $\mathcal{D}$, when over-posed boundary data are available. Following the main idea of the Method of Variational Imbedding (MVI), we “imbed” the inverse problem into a fourth-order elliptic boundary value problem ...
Christo I. Christov, Rossitza S. Marinova, Tchavdar T. Marinov   +2 more
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Elliptic partial differential equation and optimal control

Numerical Methods for Partial Differential Equations, 1992
AbstractThe theory of optimal control and the semianalytical method of elliptic partial differential equation (PDE) in a prismatic domain are mutually simulated issues. The simulation of discrete‐time linear quadratic (LQ) control with the substructural chain problem in static structural analysis is given first.
Zhong Xiang-Xiang, Zhong Wan-xie
openaire   +3 more sources

Elliptic Partial Differential Equations of Second Order

1997
We study in this chapter a class of partial differential equations that generalize and are to a large extent represented by Laplace’s equation. These are the elliptic partial differential equations of second order. A linear partial differential operator L defined by $$ Lu{\text{: = }}{a_{ij}}\left( x \right){D_{ij}}u + {b_i}\left( x \right){D_i}u +
Alan R. Elcrat, Piero Bassanini
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Elliptic Partial Differential Equations

2018
Let us consider the three-dimensional regular domain \(D\subset R^3\) bounded by the Liapunov surface \(S=\partial D\). In the classical mathematical analysis the following formula is proved which is called the Gauss-Ostrogradski-Green’s formula.
Andreas Öchsner, Marin Marin
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Elliptic Partial Differential Equation involving singularity

, 2017
The aim of this paper is to prove existence of solutions for a partial differential equation involving a singularity with a general nonnegative, Radon measure as source term which is given as \begin{eqnarray} -\Delta u &=& f(x)h(u)+\mu~\text{in}~\Omega ...
A. Panda, Sekhar Ghosh, D. Choudhuri
semanticscholar   +1 more source

Parameter identification for an elliptic partial differential equation with distributed noisy data

, 1999
This paper is devoted to the identification of a parameter in an elliptic partial differential equation from noisy distributed data. It can be divided into two parts.
R. Luce, S. Perez
semanticscholar   +1 more source

A topological approach to nonlocal elliptic partial differential equations on an annulus

Mathematische Nachrichten, 2020
For q≥1 we consider the nonlocal ordinary differential equation −a∫01|y|qdsy′′(t)=λf(t,y(t ...
C. Goodrich
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Direct phase estimation from phase differences using fast elliptic partial differential equation solvers.

Optics Letters, 1989
Obtaining robust phase estimates from phase differences is a problem common to several areas of importance to the optics and signal-processing communities.
D. Ghiglia, Louis A. Romero
semanticscholar   +1 more source