General relative entropy inequality: an illustration on growth models

By Philippe Michel, St'ephane Mischler, Benoit Perthame. 2005

267 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3570e24e3b3d4baa842d3cdfe97111f884d3db98

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In Applied Mathematics

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Diffusive and nondiffusive population models (2010, unknown): “[107].”
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations (2010, background): “The problem of convergence to self-similarity for the fragmentation equation (20) was studied in [4], and then in [10].”
Eigenelements of a General Aggregation-Fragmentation Model (2009, methodology): “For the eigenvectors we use the General Relative Entropy method introduced in [28, 29].”
A non‐conservative Harris ergodic theorem (2019, background): “This question attracted a lot of attention in the last decades, [16, 22, 38, 76, 77, 83] to mention only a few.”
Spectral analysis of semigroups and growth-fragmentation equations (2013, methodology): “It also improves the convergence results without rate obtained in [79, 34] which have been established under similar assumptions to those made in the present work.”
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−λ0t ≈ N(x) is valid [26], with λ0 > 0, and where (λ0, N) is the dominant eigenpair related to the corresponding eigenvalue problem, see [25, 27, 9, 22, 5, 1].”
Exponential decay for the growth-fragmentation/cell-division equation (2009, background): “We recall from [12, 14, 16] and the references therein that the relative entropy inequality for equation (1) reads d dt ∫ ∞”
Coagulation, fragmentation and growth processes in a size structured population (2009, background): “We note that recently there has been an interest in studying fragmentation and, in general, population type equations in another weighted L1 space where the weight is given by the first eigenfunction of the adjoint problem, possibly up to a suitable normalization, see [24, 26] and [25, Chapter 3].”