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Journal Articles Journal of Mathematical Analysis and Applications Year : 2013

Cauchy problem for multiscale conservation laws: Application to structured cell populations

Abstract

In this paper, we study a vector conservation law that models the growth and selection of ovarian follicles. This work is motivated by a multiscale mathematical model. A two-dimensional conservation law describes the age and maturity structuration of the follicular cell populations. The densities interact through a coupled hyperbolic system between different follicles and cell phases, which results in a vector conservation law and coupling between boundary conditions. The maturity velocity functions possess both a local and a nonlocal character. We prove the existence and uniqueness of the weak solution to Cauchy problem with bounded initial and boundary data.

Dates and versions

hal-00841184 , version 1 (04-07-2013)

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Peipei Shang. Cauchy problem for multiscale conservation laws: Application to structured cell populations. Journal of Mathematical Analysis and Applications, 2013, 401 (2), pp.896 - 920. ⟨10.1016/j.jmaa.2013.01.001⟩. ⟨hal-00841184⟩
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