[Non-existence de solutions locales pour les équations de la chaleur semi-linéaires de type Osgood dans des domaines bornés]
Nous établissons un résultat de non-existence locale pour l'équation avec des conditions aux limites de Dirichlet sur un domaine borné lisse et des données initiales dans lorsque le terme de source f est non décroissant et pour un exposant . Ceci nous permet de construire un f localement Lipschitz qui satisfait la condition de Osgood , ce qui garantit l'existence globale pour des données initiales dans , de telle sorte que pour chaque q tel que il existe une condition initiale non négative pour laquelle le problème semi-linéaire correspondant n'admet pas de solution locale en temps ( « blow-up immédiat »).
We establish a local non-existence result for the equation with Dirichlet boundary conditions on a smooth bounded domain and initial data in when the source term f is non-decreasing and for some exponent . This allows us to construct a locally Lipschitz f satisfying the Osgood condition , which ensures global existence for initial data in , such that for every q with there is a non-negative initial condition for which the corresponding semilinear problem has no local-in-time solution (‘immediate blow-up’).
Accepté le :
Publié le :
Robert Laister 1 ; James C. Robinson 2 ; Mikolaj Sierżęga 2
@article{CRMATH_2014__352_7-8_621_0, author = {Robert Laister and James C. Robinson and Mikolaj Sier\.z\k{e}ga}, title = {Non-existence of local solutions of semilinear heat equations of {Osgood} type in bounded domains}, journal = {Comptes Rendus. Math\'ematique}, pages = {621--626}, publisher = {Elsevier}, volume = {352}, number = {7-8}, year = {2014}, doi = {10.1016/j.crma.2014.05.010}, language = {en}, }
TY - JOUR AU - Robert Laister AU - James C. Robinson AU - Mikolaj Sierżęga TI - Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains JO - Comptes Rendus. Mathématique PY - 2014 SP - 621 EP - 626 VL - 352 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2014.05.010 LA - en ID - CRMATH_2014__352_7-8_621_0 ER -
%0 Journal Article %A Robert Laister %A James C. Robinson %A Mikolaj Sierżęga %T Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains %J Comptes Rendus. Mathématique %D 2014 %P 621-626 %V 352 %N 7-8 %I Elsevier %R 10.1016/j.crma.2014.05.010 %G en %F CRMATH_2014__352_7-8_621_0
Robert Laister; James C. Robinson; Mikolaj Sierżęga. Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains. Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 621-626. doi : 10.1016/j.crma.2014.05.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.05.010/
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