scholarly journals Jordan canonical forms for systems of elliptic equations

2021 ◽  
pp. 100006
Author(s):  
Mosito Lekhooana ◽  
Motlatsi Molati ◽  
Celestin Wafo Soh
Keyword(s):  
Elliptic Equations ◽  
Canonical Forms ◽  
Systems Of Elliptic Equations

On the Solvability of Some Nonlinear Systems of Elliptic Equations

2001 ◽  
Vol 1 (2) ◽  
Author(s):  
A.M. Piccirillo ◽  
L. Toscano ◽  
S. Toscano
Keyword(s):  
Nonlinear Systems ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Systems Of Elliptic Equations

AbstractWe study the solvability and the existence of multiple solutions of nonlinear systems of elliptic equations.

A global random walk on grid algorithm for second order elliptic equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Karl K. Sabelfeld ◽  
Dmitry Smirnov ◽  
Ivan Dimov ◽  
Venelin Todorov
Keyword(s):  
Random Walk ◽  
Elliptic Equations ◽  
Linear Equations ◽  
Computational Cost ◽  
Transition Matrices ◽  
Systems Of Linear Equations ◽  
Systems Of Elliptic Equations ◽  
Grid Algorithm ◽  
Large Systems ◽  
Second Order Elliptic Equations

Abstract In this paper we develop stochastic simulation methods for solving large systems of linear equations, and focus on two issues: (1) construction of global random walk algorithms (GRW), in particular, for solving systems of elliptic equations on a grid, and (2) development of local stochastic algorithms based on transforms to balanced transition matrix. The GRW method calculates the solution in any desired family of prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman–Kac formula. The use in local random walk methods of balanced transition matrices considerably decreases the variance of the random estimators and hence decreases the computational cost in comparison with the conventional random walk on grids algorithms.

Switched diffusion processes and systems of elliptic equations: a Dirichlet space approach

1994 ◽  
Vol 124 (4) ◽  
pp. 673-701 ◽  
Author(s):  
Z. Q. Chen ◽  
Z. Zhao
Keyword(s):  
Diffusion Process ◽  
Elliptic Equations ◽  
Diffusion Processes ◽  
Dirichlet Space ◽  
Coupled System ◽  
System A ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Systems Of Elliptic Equations ◽  
Space Approach

The switched diffusion process associated with a weakly coupled system of elliptic equations is studied via a Dirichlet space approach and is applied to prove the existence theorem of the Cauchy initial problem for the system. A representation theorem for the solution of the Dirichlet boundary value problem and a generalised Skorohod decomposition for the reflecting switched diffusion process are obtained.

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