Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation
Dias, João-Paulo ; Figueira, Mário
Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000), p. 739-750 / Harvested from Biblioteca Digitale Italiana di Matematica
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Si considera il problema di Cauchy per l'equazione (cf. [1]): ϕt⁢t-ϕx⁢x-ϕx2⁢ϕx⁢x+sin⁡ϕ=0⁢x,t∈R×R+. Nella prima parte di questo articolo si dimostra, per dati iniziali particolari, un risultato di «blow-up» della soluzione classica locale (in tempo), seguendo le idee introdotte in [8], [2] ed [4]. Nella seconda parte, viene utilizzato il metodo di compattezza per compensazione (cf. [13], [10] ed [5]) ed una estensione del principio delle regioni invarianti (cf. [12]) per dimostrare l'esistenza di una soluzione debole globale entropica.

Publié le : 2000-10-01
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     author = {Jo\~ao-Paulo Dias and M\'ario Figueira},
     title = {Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3-A},
     year = {2000},
     pages = {739-750},
     zbl = {0962.35022},
     mrnumber = {1801606},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_3_739_0}
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Dias, João-Paulo; Figueira, Mário. Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 739-750. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_3_739_0/

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