ON CERTAIN NONLOCAL PROBLEM WITH MIXED BOUNDARY CONDITION FOR A PARABOLIC SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS

1982 ◽  
Vol 15 (3) ◽  
Author(s):  
Marian Majchrowski
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Parabolic System ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Nonlocal Problem ◽  
Partial Differential

scholarly journals Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 332 ◽  
Author(s):  
Hamza Medekhel ◽  
Salah Boulaaras ◽  
Khaled Zennir ◽  
Ali Allahem
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Parabolic System ◽  
Stationary Case ◽  
Partial Differential ◽  
Existence Of Positive Solutions

This paper deals with the existence of positively solution and its asymptotic behavior for parabolic system of ( p ( x ) , q ( x ) ) -Laplacian system of partial differential equations using a sub and super solution according to some given boundary conditions, Our result is an extension of Boulaaras’s works which studied the stationary case, this idea is new for evolutionary case of this kind of problem.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

STEADY FLOW OF FLUIDS WITH SHEAR-DEPENDENT VISCOSITY UNDER MIXED BOUNDARY VALUE CONDITIONS IN POLYHEDRAL DOMAINS

2000 ◽  
Vol 10 (05) ◽  
pp. 629-650 ◽  
Author(s):  
C. EBMEYER
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Steady Flow ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Partial Differential ◽  
Shear Dependent Viscosity ◽  
Polyhedral Domain ◽  
Dependent Viscosity

In this paper the system of partial differential equations [Formula: see text] is studied, where e is the symmetrized gradient of u, and T has p-structure for some p<2 (e.g. div T is the p-Laplacian and p<2). Mixed boundary value conditions on a three-dimensional polyhedral domain are considered. Ws,p-regularity (s=3/2-ε) of the velocity u and Wr,p′-regularity of the pressure π are proven.

Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application

2006 ◽  
Vol 128 (4) ◽  
pp. 946-959 ◽  
Author(s):  
Nhan Nguyen ◽  
Mark Ardema
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Control Problem ◽  
Boundary Control ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

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