Existence and Stability of $$L^{p}$$ Solutions of the Steady State Magnetohydrodynamic Equations with Rough External Forces

2021 ◽  
Author(s):  
S. V. Uddhao ◽  
P. D. Raiter ◽  
R. V. Saraykar
Keyword(s):  
Steady State ◽  
Magnetohydrodynamic Equations ◽  
Existence And Stability ◽  
External Forces

scholarly journals Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy-minimization approach

2011 ◽  
Vol 57 (202) ◽  
pp. 345-354 ◽  
Author(s):  
Guillaume Jouvet ◽  
Jacques Rappaz ◽  
Ed Bueler ◽  
Heinz Blatter
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Mass Balance ◽  
Energy Minimization ◽  
Existence Of Solutions ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Existence And Stability ◽  
Steady State Solutions ◽  
Minimization Approach

AbstractThe existence of solutions of the non-sliding shallow-ice-sheet equation on a flat horizontal bed with a mass balance linearly depending on altitude is proven for fixed margins. Free-margin solutions for the same mass balance do not exist. Fixed-margin solutions show unbounded shear stress and nonzero mass flux at the margin. Steady-state solutions with realistic margins, vanishing ice flux and vanishing shear stress are found numerically for ice sheets with Weertman-type sliding.

scholarly journals Steady state analysis of a syntrophic model: the effect of a new input substrate concentration

2018 ◽  
Vol 13 (3) ◽  
pp. 31
Author(s):  
Y. Daoud ◽  
N. Abdellatif ◽  
T. Sari ◽  
J. Harmand
Keyword(s):  
Steady State ◽  
Methanogenic Bacteria ◽  
Stable Steady State ◽  
Operating Parameters ◽  
Steady State Analysis ◽  
Bacteria Growth ◽  
Digestion Process ◽  
Acetogenic Bacteria ◽  
Existence And Stability ◽  
Exponentially Stable

In this work, we are interested in a reduced and simplified model of the anaerobic digestion process. We focus on the acetogenesis and hydrogenetrophic methanogenesis phases. The model describes a syntrophic relashionship between two microbial species (the acetogenic bacteria and the hydrogenetrophic methanogenic bacteria) with two input substrates (the fatty acids and the hydrogen) including both decay terms and inhibition of the acetogenic bacteria growth by an excess of hydrogen in the system. The existence and stability analysis of the steady states of the model points out the existence of a new equilibrium point which can be stable according to the operating parameters of the system. By means of operating diagrams, we show that, whatever the region of space considered, there exists only one locally exponentially stable steady state.

Bounds for the solution of a non-linear parabolic initial-boundary value problem

1977 ◽  
Vol 82 (1) ◽  
pp. 131-145
Author(s):  
M. R. Carter
Keyword(s):  
Steady State ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value Problems ◽  
The Past ◽  
Existence And Stability ◽  
Image Position ◽  
Initial Boundary Value ◽  
Steady State Solutions

A number of papers have appeared over the past decade or so which study questions of the existence and stability of positive steady-state solutions for parabolic initial-boundary value problems of the general form

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