Some analytical results about a simple reaction-diffusion system for morphogenesis
- 1 January 1979
- journal article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 7 (4) , 375-384
- https://doi.org/10.1007/bf00275155
Abstract
The reaction-diffusion system considered involves only one nonlinear term and is a gradient system. In a bifurcation analysis for the equilibrium states, the global existence of infinitely many solution branches can be shown by the method of Ljusternik-Schnirelmann. Their stability is studied. Using a Ljapunov functional it can be shown that the solutions of the time-dependent system converge to the equilibrium states.Keywords
This publication has 12 references indexed in Scilit:
- A simple system of reaction-diffusion equations describing morphogenesis: Asymptotic behaviorAnnali di Matematica Pura ed Applicata (1923 -), 1979
- Stability results for a class of non-linear parabolic equationsAnnali di Matematica Pura ed Applicata (1923 -), 1977
- A model of pattern formation in insect embryogenesisJournal of Cell Science, 1977
- A comparison technique for systems of reaction-diffusion equationsCommunications in Partial Differential Equations, 1977
- Reaction-diffusion equation describing morphogenesis I. waveform stability of stationary wave solutions in a one dimensional modelMathematical Biosciences, 1975
- Some aspects of nonlinear eigenvalue problemsRocky Mountain Journal of Mathematics, 1973
- Solutions to Axon EquationsBiophysical Journal, 1970
- Differential and Integral InequalitiesPublished by Springer Nature ,1970
- Dynamical systems and stabilityJournal of Mathematical Analysis and Applications, 1969
- The chemical basis of morphogenesisPhilosophical Transactions of the Royal Society of London. B, Biological Sciences, 1952