Geodesic
Local existence and estimations for a semilinear wave equation in two dimension space
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 1-21

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we prove a local existence theorem for a Cauchy problem associated to a semi linear wave equation with an exponential nonlinearity in two dimension space. In this problem, the first Cauchy data is equal to zero, the second is in $L^{2}(\mathbb{R}^{2})$, radially symmetric and compactly supported. To prove this theorem, we first show a Moser-Trudinger type inequality for the linear problem and then we use a fixed point method to achieve the proof of the result. 
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     author = {Baraket, Amel Atallah},
     title = {Local existence and estimations for a semilinear wave equation in two dimension space},
     journal = {Bollettino della Unione matematica italiana},
     pages = {1--21},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {1},
     year = {2004},
     zbl = {1117.35046},
     mrnumber = {MR2044259},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a0/}
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Baraket, Amel Atallah. Local existence and estimations for a semilinear wave equation in two dimension space. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 1-21. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a0/