EXISTENCE OF A SOLUTION TO THE CELL DIVISION EIGENPROBLEM

By Philippe Michel. 2006

94 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f9ccd99c0615c8c5fe0edaffb7b00d2228887cb8

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Citations in the corpus

Limit theorems for some branching measure-valued processes (2011, background): “Some criteria for the existence of eigenelements can be found in [3], [12], [37], [41], and the references therein.”
Spectral analysis of semigroups and growth-fragmentation equations (2013, methodology): “It is also likely that our approach can be generalized to larger classes of growth operator and of fragmentation kernel as those considered in [77, 30, 19, 8] for instance.”
Exponential decay for the growth-fragmentation/cell-division equation (2009, background): “ady renormalised so that zero is the ﬁrst eigenvalue of the underlying linear integro-diﬀerential operator. Indeed, recall that, under fairly general assumptions on κ that were stated for instance in [11, 14], there exists a unique steady state N ∈ L1(0,∞) satisfying ∂ ∂x N(x) +kBN(x) = B Z ∞ 0”
On the foundations of cancer modelling: Selected topics, speculations, and perspectives (2008, background): “See, for example, De Angelis and Jabin,(61,62) Derbel,(64) Bellouquid and Delitala,(33,35) Micheler, Perthame and Ryzhik,(144) and Michel.(143)”
Eigenelements of a General Aggregation-Fragmentation Model (2009, background): “The paper [26] gives results for τ(0) = 0, but for a very restricted class of shape for τ.”
Statistical estimation of a growth-fragmentation model observed on a genealogical tree (2012, methodology): “By use of the general relative entropy principle, Michel, Mischler and Perthame showed that the approximation n ( t, x ) e − λ 0 t ≈ N ( x ) is valid [29], with λ 0 > 0, and where ( λ 0 , N ) is the dominant eigenpair related to the corresponding eigenvalue problem, see [28, 32, 12, 25, 8, 2].”
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations (2010, background): “However, this modification is not essential, and the results in [3] show the following (see also the truncated problems in [8], [12]): Lemma 4.”
A non‐conservative Harris ergodic theorem (2019, methodology): “ to ﬁrst solve the Perron eigenvalue problem and then prove the (exponential) convergence. This strategy also applies for more general fragmentation kernels. The eigenvalue problem has been solved in [56, 31] for general coeﬃcients. Then, the General Relative Entropy technique developed by Michel, M”