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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.
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https://hal.inria.fr/hal-00841184
Contributor : Frederique Clement <>
Submitted on : Thursday, July 4, 2013 - 10:03:50 AM
Last modification on : Saturday, June 19, 2021 - 3:50:30 AM

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

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