Sledování nemódních cílů
Mean square value of exponential sums related to representation of integers as sum of two squares
Mean square limit for lattice points in a sphere
Erratum to the paper "Mean square limit for lattice points in a sphere" (Acta Arith. 68 (1994), 383-393)
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in -dimensional space. We prove the existence of solutions, which exist globally, and are -bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes
A model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of...
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