6533b85cfe1ef96bd12bc808
RESEARCH PRODUCT
Existence and uniqueness results for a nonlinear evolution equation arising in growing cell populations
Ahmed ZeghalKhalid LatrachJesús Garcia-falsetsubject
education.field_of_studyCell divisionDegree (graph theory)Applied MathematicsPopulationMathematical analysisNonlinear systemUniquenessBoundary value problemeducationNonlinear evolutionValue (mathematics)AnalysisMathematicsdescription
Abstract The present paper is concerned with a nonlinear initial–boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by two parameters: its degree of maturity μ and its maturation velocity v . At mitosis, the daughter cells and mother cells are related by a general reproduction rule. We prove existence and uniqueness results in the case where the total cross-section and the boundary conditions are depending on the total density of population. Local and nonlocal reproduction rules are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-03-01 | Nonlinear Analysis: Theory, Methods & Applications |