Comparison principle for a set of equations with a robust causal operator

2009 ◽  
Vol 80 (1) ◽  
pp. 602-605 ◽  
Author(s):  
A. A. Martynyuk
Keyword(s):  
Comparison Principle ◽  
Causal Operator

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

On the Cauchy problem associated with the Brinkman flow in

2021 ◽  
pp. 1-20
Author(s):  
Michel Molina Del Sol ◽  
Eduardo Arbieto Alarcon ◽  
Rafael José Iorio
Keyword(s):  
Cauchy Problem ◽  
Porous Media ◽  
Fluid Flow ◽  
Comparison Principle ◽  
Well Posedness ◽  
Quasilinear Equations ◽  
Brinkman Equations ◽  
The Cauchy Problem ◽  
Model Fluid ◽  
Image Position

In this study, we continue our study of the Cauchy problem associated with the Brinkman equations [see (1.1) and (1.2) below] which model fluid flow in certain types of porous media. Here, we will consider the flow in the upper half-space \[ \mathbb{R}_{+}^{3}=\left\{\left(x,y,z\right) \in\mathbb{R}^{3}\left\vert z\geqslant 0\right.\right\}, \] under the assumption that the plane $z=0$ is impenetrable to the fluid. This means that we will have to introduce boundary conditions that must be attached to the Brinkman equations. We study local and global well-posedness in appropriate Sobolev spaces introduced below, using Kato's theory for quasilinear equations, parabolic regularization and a comparison principle for the solutions of the problem.

scholarly journals A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians

2011 ◽  
Vol 139 (05) ◽  
pp. 1777-1777 ◽  
Author(s):  
Yoshikazu Giga ◽  
Przemysław Górka ◽  
Piotr Rybka
Keyword(s):  
Comparison Principle ◽  
Jacobi Equations

Cylindrical optimal rearrangement problem leading to a new type obstacle problem

2018 ◽  
Vol 24 (2) ◽  
pp. 859-872 ◽  
Author(s):  
Hayk Mikayelyan
Keyword(s):  
Comparison Principle ◽  
Obstacle Problem ◽  
Normal Derivative ◽  
Force Function ◽  
Cylindrical Domain ◽  
New Type ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Cylindrical Axis

An optimal rearrangement problem in a cylindrical domainΩ=D× (0, 1) is considered, under the constraint that the force function does not depend on thexnvariable of the cylindrical axis. This leads to a new type of obstacle problem in the cylindrical domain     Δu(x′,xn) =χ{v>0}(x′) +χ{v=0}(x′) [∂νu(x′,0) +∂νu(x′, 1)]arising from minimization of the functional     ∫Ω½;|∇u(x)|2+χ{v>0}(x′)u(x) dx,wherev(x′) =∫01u(x′,t)dt, and∂νuis the exterior normal derivative ofuat the boundary. Several existence and regularity results are proven and it is shown that the comparison principle does not hold for minimizers.

Sign in / Sign up

Export Citation Format

Share Document