Differential and Integral Equations

Positive solutions to a system of periodic parabolic partial differential equations

Afshin Ghoreishi and Roger Logan

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Abstract

We use the methods of [24, 15] to provide an extension of results presented in [7, 16, 24] to derive existence of positive solutions to a general system of periodic parabolic equations which arise in the study of population dynamics. We will consider the following system with mixed boundary conditions. $$ \begin{align} u_t(x,t)-d_1(x,t)\Delta u(x,t)&= u(x,t)M(x,t,u,v) \\ v_t(x,t)-d_2(x,t)\Delta v(x,t)&= v(x,t)N(x,t,u,v). \end{align} $$

Article information

Source
Differential Integral Equations, Volume 9, Number 3 (1996), 607-618.

Dates
First available in Project Euclid: 7 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367969975

Mathematical Reviews number (MathSciNet)
MR1371711

Zentralblatt MATH identifier
0852.35061

Subjects
Primary: 35K50
Secondary: 35B10: Periodic solutions 35K55: Nonlinear parabolic equations 35Q80: PDEs in connection with classical thermodynamics and heat transfer 92D25: Population dynamics (general)

Citation

Ghoreishi, Afshin; Logan, Roger. Positive solutions to a system of periodic parabolic partial differential equations. Differential Integral Equations 9 (1996), no. 3, 607--618. https://projecteuclid.org/euclid.die/1367969975


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