Publication: Análisis matemático de un modelo de ecuaciones en derivadas parciales con términos quimiotácticos
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2021-05-12
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Universidad Complutense de Madrid
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Abstract
En esta tesis analizamos las propiedades de un conjunto de sistemas de Ecuaciones en Derivadas Parciales que modelan varios fenomenos de la biologa, tanto desde el punto de vista del analisis matematico como del analisis numerico. Los modelos presentan terminos de crecimiento logístico con un comportamiento periodico tienden a un comportamiento periodico. Se abordan los sistemas parabolico-elptico, parabolico-parabolico y parabolico-ordinario. En la tesis se obtienen resultados sobre la existencia global de las soluciones, su límite uniforme y su comportamiento asintotico periodico uniforme. Los sistemas de quimiotaxis presentan una no linealidad de segundo orden (en las derivadas) donde radica la principal dificultad del problema...
In this thesis we analyze the properties of a set of systems of Partial Dierential Equations which model various phenomena in biology, both from the point of view of mathematical analysis and numerical analysis.The models present terms of logistic growth with periodic behavior or tend towards a periodic behavior. Parabolic-elliptic, parabolic-parabolic and parabolic-ordinary systems are addressed. In the thesis, the results are obtained on the global existence of solutions, their uniform boundedness and their periodic uniform asymptotic behavior. The systems of chemotaxis present a non-linearity of second order (in the derivatives) where the main difficulty of the problem lies...
In this thesis we analyze the properties of a set of systems of Partial Dierential Equations which model various phenomena in biology, both from the point of view of mathematical analysis and numerical analysis.The models present terms of logistic growth with periodic behavior or tend towards a periodic behavior. Parabolic-elliptic, parabolic-parabolic and parabolic-ordinary systems are addressed. In the thesis, the results are obtained on the global existence of solutions, their uniform boundedness and their periodic uniform asymptotic behavior. The systems of chemotaxis present a non-linearity of second order (in the derivatives) where the main difficulty of the problem lies...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 18-12-2020