Analysis of a nonlinear necrotic tumor model with angiogenesis and a periodic supply of external nutrients

Autor: Song, Huijuan, Huang, Qian, Wang, Zejia

In this paper, we consider a free boundary problem modeling the growth of spherically symmetric necrotic tumors with angiogenesis and a $\omega$-periodic supply $\phi(t)$ of external nutrients. In the model, the consumption rate of the nutrient and t

Externí odkaz: http://arxiv.org/abs/2110.04688

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

Autor: Brauner, Claude-Michel, Hu, Lina, Lorenzi, Luca

We consider a free interface problem which stems from a solid-gas model in combustion with pattern formation. We derive a third-order, fully nonlinear, self-consistent equation for the flame front. Asymptotic methods reveal that the interface approac

Externí odkaz: http://arxiv.org/abs/1211.0678

Nondegeneracy for stable solutions to the one-phase free boundary problem

Autor: Nikola Kamburov, Kelei Wang

We prove the nondegeneracy condition for stable solutions to the one-phase free boundary problem. The proof is by a De Giorgi iteration, where we need the Sobolev inequality of Michael and Simon and, consequently, an integral estimate for the mean cu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::833a1effa5fd0ecd077bfcc516ecea82
http://arxiv.org/abs/2207.12740

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

Autor: Luca Lorenzi, Lina Hu, Claude-Michel Brauner

Publikováno v: Chinese Annals of Mathematics-Series B
Chinese Annals of Mathematics-Series B, Springer Verlag, 2013, 34 (1), pp.24. ⟨10.1007/s11401-012-0758-4⟩

We consider a free interface problem which stems from a solid-gas model in combustion with pattern formation. We derive a third-order, fully nonlinear, self-consistent equation for the flame front. Asymptotic methods reveal that the interface approac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::273572f9addae9b45997c999e33982eb

On the transverse instability of one dimensional capillary-gravity waves

Autor: Nikolay Tzvetkov, Frédéric Rousset

Publikováno v: Discrete and Continuous Dynamical Systems-Series B
Discrete and Continuous Dynamical Systems-Series B, American Institute of Mathematical Sciences, 2010, 13 (4), pp.859-872
Discrete and Continuous Dynamical Systems-Series B, 2010, 13 (4), pp.859-872. ⟨10.3934/dcdsb.2010.13.859⟩

International audience; This text represents the content of a talk given by the second author at ENS Paris on January 28, 2009 at the conference "Mathematics and Oceanography". We are grateful to David Gerard-Varet, David Lannes and Laure Saint-Raymo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::142939385354f3bb0b79b577a67a262f
https://hal.archives-ouvertes.fr/hal-00521628