Qualitative analysis of a coupled reaction-diffusion model in biology with time delays

DOI10.1016/0022-247X(85)90156-8zbMath0583.92012OpenAlexW2031207886MaRDI QIDQ1069461

Chia-Ven Pao, Joseph M. Mahaffy

Publication date: 1985

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(85)90156-8

zbMATH Keywords

lower and upper solutionsnucleusstationary solutioncytoplasmmRNAbiochemical reactionthree-compartment modelcoupled system of delay-differential and reaction-diffusion equationsGoodwin model for biochemical control of geneslinear parabolic partial differential equationsmembrane exchangesnegative feedback mechanismrepressor proteintime-delayed ordinary differential equations

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Physiological, cellular and medical topics (92Cxx)

Related Items (9)

Interaction of spatial diffusion and delays in models of genetic control by repression ⋮ Oscillations and multiple steady states in a cyclic gene model with repression ⋮ Reaction-diffusion problems in cell tissues ⋮ Combined iterative methods for numerical solutions of parabolic problems with time delays ⋮ Traveling wavefronts for a time delayed non-Newtonian filtration equation ⋮ On global stability of parabolic systems with delay ⋮ Finite difference reaction-diffusion systems with coupled boundary conditions and time delays ⋮ Separable models in age-dependent population dynamics ⋮ Models of genetic control by repression with time delays and spatial effects

Cites Work

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• A global stability criterion for simple control loops
• Reaction diffusion equations with nonlinear boundary conditions
• A Boltzmann-type equation in the kinetic theory of vehicular traffic
• Global asymptotic stability of certain models for protein synthesis and repression

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