Derivation of FBs for tumor growth - 2

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Description:	Perthame, B (Université Pierre et Marie Curie) Monday 06 January 2014, 13:30-14:30


Created:	2014-01-08 10:12
Collection:	Free Boundary Problems and Related Topics
Publisher:	Isaac Newton Institute
Copyright:	Perthame, B
Language:	eng (English)


Abstract:	The example of invasion fronts - The approach based on Hamilton-Jacobi equations - Accelerating fronts - The tail problem When used for biology and medicine, PDEs have to be used with care. Even though some are very classical, as front propagation for invading species, they are always questioned by comparison to observations or experiments. This course aims at showing some examples of free boundary problems motivated by biology and medicine, to concentrate on weak solutions, and to discuss their limitations and the need for further developments. Suggested reading [1] M. Belhadj, J.-F. Gerbeau and B. Perthame. A multiscale transport model of colloids with degenerate anisotropic diffusion. Asymptotic Analysis 34(1) (2003) 41--54. [2] G. Barles and P.E. Souganidis. Front propagation for reaction-diffusion equations arising in combustion theory. Asymptot. Anal., 14:277292, 1997. [3] A. Lorz, B. Perthame, P. Markowich, Bernoulli variational problem and beyond. To appear in ARMA (2014). http://hal.upmc.fr/hal-00881760 [4] B. Perthame, F. Quiros, J.-L. Vazquez, The Hele-Shaw asymptotics for mechanical models of tumor growth. To appear in ARMA (2014) http://hal.upmc.fr/hal-00831932 [5] Emeric Bouin, Vincent Calvez, Nicolas Meunier, Sepideh Mirrahimi, Benoît Perthame, Gael Raoul, and Raphaël Voituriez. Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. C. R. Math. Acad. Sci. Paris, 350(15-16):761766, 2012.

Abstract:

The example of invasion fronts - The approach based on Hamilton-Jacobi equations - Accelerating fronts - The tail problem

When used for biology and medicine, PDEs have to be used with care. Even though some are very classical, as front propagation for invading species, they are always questioned by comparison to observations or experiments. This course aims at showing some examples of free boundary problems motivated by biology and medicine, to concentrate on weak solutions, and to discuss their limitations and the need for further developments.

Suggested reading

[1] M. Belhadj, J.-F. Gerbeau and B. Perthame. A multiscale transport model of colloids with degenerate anisotropic diffusion. Asymptotic Analysis 34(1) (2003) 41--54.

[2] G. Barles and P.E. Souganidis. Front propagation for reaction-diffusion equations arising in combustion theory. Asymptot. Anal., 14:277292, 1997.

[3] A. Lorz, B. Perthame, P. Markowich, Bernoulli variational problem and beyond. To appear in ARMA (2014). http://hal.upmc.fr/hal-00881760

[4] B. Perthame, F. Quiros, J.-L. Vazquez, The Hele-Shaw asymptotics for mechanical models of tumor growth. To appear in ARMA (2014) http://hal.upmc.fr/hal-00831932

[5] Emeric Bouin, Vincent Calvez, Nicolas Meunier, Sepideh Mirrahimi, Benoît Perthame, Gael Raoul, and Raphaël Voituriez. Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. C. R. Math. Acad. Sci. Paris, 350(15-16):761766, 2012.

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