A Fokker-Planck equation for growing cell populations

DOI10.1007/BF00275888zbMath0644.92019OpenAlexW1964566566WikidataQ52428630 ScholiaQ52428630MaRDI QIDQ1102891

Cornelis V. M. van der Mee, Paul F. Zweifel

Publication date: 1987

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00275888

zbMATH Keywords

Fokker-Planck equationclosed form solutionsseparation of variableseigenfunction expansionsAiry functionsdegree of maturitymaturation velocitymodel for cell growthreproduction equationtime dependent linear transport theory

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Explicit solutions, first integrals of ordinary differential equations (34A05) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (15)

Global Bifurcation from the Real Leading Eigenvalue of the Transport Operator ⋮ Time asymptotic behaviour for unbounded linear operators arising in growing cell populations. ⋮ Existence and uniqueness results for a nonlinear evolution equation arising in growing cell populations ⋮ Symmetry properties of conservation laws for nonlinear Fokker-Planck equation describing cell population growth ⋮ A nonlinear structured population model of tumor growth with quiescence ⋮ EXISTENCE RESULTS FOR A BOUNDARY VALUE PROBLEM ARISING IN GROWING CELL POPULATIONS ⋮ A mathematical study for a Rotenberg model ⋮ Spectral analysis of a transport operator arising in growing cell populations ⋮ Some Fixed Point Theorems and Application to Biological Model ⋮ On a nonlinear version of Rotenberg model with infinite maturation velocities ⋮ Stochastic branching at the edge: individual-based modeling of tumor cell proliferation ⋮ Lie symmetry analysis and invariant solutions of a nonlinear Fokker-Planck equation describing cell population growth ⋮ On a mathematical model with non-compact boundary conditions describing bacterial population. II ⋮ Existence results for a nonlinear version of Rotenberg model with infinite maturation velocities ⋮ Time asymptotic behavior of the solution to a Cauchy problem governed by a transport operator

Cites Work

• Half-range completeness for the Fokker-Planck equation. I
• Abstract time-dependent transport equations
• A theory for the age and generation time distribution of a microbial population
• Spectral properties of the space nonhomogeneous linearized Boltzmann operator
• On the spectral decomposition of the transport operator with anisotropic scattering and periodic boundary conditions
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