0000000000730026

AUTHOR

Khalid Latrach

showing 3 related works from this author

Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

2012

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

Discrete mathematicsQuantitative Biology::Neurons and CognitionPicard–Lindelöf theoremApplied MathematicsFixed-point theoremFixed-point propertyKrasnoselskii fixed point theoremSchauder fixed point theoremNonlinear integral equationsMeasure of weak noncompactnessBrouwer fixed-point theoremKakutani fixed-point theoremContraction (operator theory)Nonlinear operatorsAnalysisMathematicsJournal of Differential Equations
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Existence and uniqueness results for a nonlinear evolution equation arising in growing cell populations

2014

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.

education.field_of_studyCell divisionDegree (graph theory)Applied MathematicsPopulationMathematical analysisNonlinear systemUniquenessBoundary value problemeducationNonlinear evolutionValue (mathematics)AnalysisMathematicsNonlinear Analysis: Theory, Methods & Applications
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An existence and uniqueness principle for a nonlinear version of the Lebowitz-Rubinow model with infinite maximum cycle length

2017

The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.

education.field_of_studyGeneral Mathematics010102 general mathematicsMathematical analysisPopulationGeneral EngineeringNonlocal boundary01 natural sciences010101 applied mathematicsNonlinear systemPopulation modelUniqueness0101 mathematicsNonlinear evolutioneducationValue (mathematics)Cycle lengthMathematicsMathematical Methods in the Applied Sciences
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