Existence of a Periodic Solution in the Form of a Two-Dimensional Front in a System of Parabolic Equations

2020 ◽  
Vol 56 (4) ◽  
pp. 462-477 ◽  
Author(s):  
A. A. Melnikova ◽  
N. N. Deryugina
Keyword(s):  
Periodic Solution ◽  
Parabolic Equations ◽  
Two Dimensional ◽  
System Of Parabolic Equations

scholarly journals Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Weibing Wang ◽  
Jianhua Shen ◽  
Juan J. Nieto
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Effect ◽  
Two Dimensional ◽  
Stable Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Stable Periodic ◽  
Holling Type Functional Response

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

scholarly journals Multidimensional computational models of gas combustion in heterogeneous porous medium

2021 ◽  
Vol 2099 (1) ◽  
pp. 012010
Author(s):  
Yu Laevsky ◽  
T Nosova
Keyword(s):  
Porous Medium ◽  
Parabolic Equations ◽  
Computational Models ◽  
Front Propagation ◽  
Original Model ◽  
Gas Mixture ◽  
Heterogeneous Porous Medium ◽  
Gas Combustion ◽  
Piecewise Constant ◽  
System Of Parabolic Equations

Abstract The processes of filtration gas combustion in heterogeneous porous medium is studying. The presence of two opposite modes of front propagation made it possible to stabilize the combustion front in a composite porous medium with piecewise constant porosity. A feature of this study is the presentation of the original model not in the traditional form of a system of parabolic equations, but in the form of integral conservation laws in terms of the temperature of the porous medium, the total gas enthalpy, and the mass of gas mixture, and the fluxes corresponding to these functions.

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