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.
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@article{CRMATH_2017__355_3_290_0, author = {Escobedo, Miguel}, title = {A short remark on a growth{\textendash}fragmentation equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {290--295}, publisher = {Elsevier}, volume = {355}, number = {3}, year = {2017}, doi = {10.1016/j.crma.2017.01.013}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2017.01.013/} }
TY - JOUR AU - Escobedo, Miguel TI - A short remark on a growth–fragmentation equation JO - Comptes Rendus. Mathématique PY - 2017 SP - 290 EP - 295 VL - 355 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2017.01.013/ DO - 10.1016/j.crma.2017.01.013 LA - en ID - CRMATH_2017__355_3_290_0 ER -
Escobedo, Miguel. A short remark on a growth–fragmentation equation. Comptes Rendus. Mathématique, Tome 355 (2017) no. 3, pp. 290-295. doi : 10.1016/j.crma.2017.01.013. http://archive.numdam.org/articles/10.1016/j.crma.2017.01.013/
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