Journal article
Necessary condition for the existence of periodic solutions to systems of reaction-diffusion equations
Mathematical biosciences, v 21(3), pp 345-350
1974
Abstract
It is shown that periodic solutions
c
i
=
c
i
(
x,
t)≡
c
i
(
x,
t+
T) to systems of reaction-diffusion equations of the form
∂c
i
∂t
=D
iλ
2c
i+
Q
i(c)
are such that the average over a period of a certain functional of the
c
i
's vanishes if the boundary conditions are such that each
c
i
is independent of time or its normal derivative vanishes at all boundary points. Sufficient to preclude a periodic solution immediately if
∂
Q
i(c)
∂c
j
=∂
Q
j(c)/∂c
j
, this necessary condition for the existence of periodic solutions also provides a useful criterion in the general case. A special application of the necessary condition is presented for periodic running wave solutions with
c
i
=
c
i
(
t−
f(
x))≡
c
i
(
t−
f(
x)+
T).
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2 citations in Scopus
Details
- Title
- Necessary condition for the existence of periodic solutions to systems of reaction-diffusion equations
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Mathematical biosciences, v 21(3), pp 345-350
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Scopus ID
- 2-s2.0-0016162840
- Other Identifier
- 991019174630804721