Comptes Rendus
Partial differential equations
A short remark on a growth–fragmentation equation
[Une brève remarque sur une équation de croissance–fragmentation]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 290-295.

Nous obtenons une solution explicite d'une équation de croissance–fragmentation avec mesure de dislocation constante. Dans cet exemple, la condition nécessaire sous laquelle les résultats généraux d'existence de solutions globales sont obtenus dans [5] pour le cas dit self-similaire n'est pas satisfaite. La solution est locale et explose en temps fini.

An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in [5] about the existence of global solutions in the so-called self-similar case is not satisfied. The solution is local and blows up in finite time.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.01.013

Miguel Escobedo 1

1 Departamento de Matemáticas, Universidad del País Vasco (UPV/EHU), 48080 Bilbao, Spain
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Miguel Escobedo. A short remark on a growth–fragmentation equation. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 290-295. doi : 10.1016/j.crma.2017.01.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.013/

[1] M. Abramowitz; I.A. Stegun Handbook of Mathematical Functions, Dover, New York, 1965

[2] A.M. Balk; V.E. Zakharov Stability of weak-turbulence Kolmogorov spectra (V.E. Zakharov, ed.), Nonlinear Waves and Weak Turbulence, AMS Translations Series 2, vol. 182, 1998, pp. 1-81

[3] J. Banasiak; L. Arlotti Perturbations of Positive Semigroups with Applications, Springer Monographs in Mathematics, Springer-Verlag London Limited, 2006

[4] J. Bertoin; R. Stephenson Local explosion in self-similar growth–fragmentation processes, Electron. Commun. Probab., Volume 21 (2016), pp. 21-66

[5] J. Bertoin; A.R. Watson Probabilistic aspects of critical growth–fragmentation equations, Adv. Appl. Probab., Volume 48 (2016), pp. 37-61

[6] J. Bertoin; N. Curien; I. Kortchemski Random planar maps & growth-fragmentations (Preprint, available at:) | arXiv

[7] M. Doumic; M. Escobedo Time asymptotics for a critical case in fragmentation and growth–fragmentation equations, Kinet. Relat. Models, Volume 9 (2016), pp. 251-297

[8] M. Doumic; P. Gabriel Eigenelements of a general aggregation-fragmentation model, Math. Models Methods Appl. Sci., Volume 20 (2010), pp. 757-783

[9] M. Escobedo, In preparation.

[10] O.P. Misra; J.L. Lavoine Transform Analysis of Generalized Functions, North-Holland Mathematics Studies, Elsevier Science, Amsterdam, New York, Oxford, 1986

[11] F.W. Olver; D.W. Lozier; R.F. Boisvert; C.W. Clark NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010

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