Displaying similar documents to “Mathematical models of tumor growth systems”

PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic

Benoît Perthame (2004)

Applications of Mathematics

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Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments...

Nonlocal quadratic evolution problems

Piotr Biler, Wojbor Woyczyński (2000)

Banach Center Publications

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Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation...

Mathematical modeling of antigenicity for HIV dynamics

François Dubois, Hervé V.J. Le Meur, Claude Reiss (2010)

MathematicS In Action

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This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses...