scholarly journals Existence Result for a Class of Nonlinear Elliptic Systems on Punctured Unbounded Domains

2010 ◽  
Vol 2010 (1) ◽  
pp. 175409 ◽  
Author(s):  
Fabrice Colin
Keyword(s):  
Existence Result ◽  
Unbounded Domains ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Nonlinear Elliptic

EXISTENCE OF SOLUTION TO NONLINEAR ELLIPTIC SYSTEMS ARISING IN TURBULENCE MODELLING

2000 ◽  
Vol 10 (02) ◽  
pp. 247-260 ◽  
Author(s):  
MACARENA GÓMEZ MÁRMOL ◽  
FRANCISCO ORTEGÓN GALLEGO
Keyword(s):  
Steady State ◽  
Turbulence Model ◽  
Existence Result ◽  
Elliptic Systems ◽  
Existence Of Solution ◽  
Turbulence Modelling ◽  
Drop Out ◽  
Nonlinear Elliptic Systems ◽  
Existence Of A Solution ◽  
Nonlinear Elliptic

We study some nonlinear elliptic systems governing the steady-state of a two-equation turbulence model that has been derived from the so-called k–ε model. Two kinds of problems are considered: in the first one, we drop out transport terms and we deduce the existence of a solution for [Formula: see text]; in the second one we take into account all transport terms; in this case, the existence result holds for N=2 or 3. Positivity and [Formula: see text]-regularity of the scalar quantities are also shown here.

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 823-837 ◽  
Author(s):  
A. CAÑADA ◽  
J.L. GÁMEZ
Keyword(s):  
Positive Solutions ◽  
Nonlinear Interaction ◽  
Spatial Dependence ◽  
Global Bifurcation ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Decoupling Method ◽  
Nonlinear Elliptic ◽  
Cooperative Models

In this paper we prove the existence of nonnegative and non-trivial solutions of problems of the form [Formula: see text] Our main result improves many previous results of other authors and it may be applied to study the three standard situations: competition, prey-predator and cooperative models. We also cover some other cases which, due essentially to the spatial dependence or to a nonlinear interaction, are not any of these three types. The method of proof combines a decoupling method with a global bifurcation result.

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