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.
In questo articolo dimostriamo un teorema di esistenza locale per un problema di Cauchy associato ad un'equazione delle onde semilineare in dimensione due. In questo problema la prima condizione iniziale è identicamente nulla, la seconda appartiene a $L^{2}(\mathbb{R}^{2})$, è a simmetria radiale e a supporto compatto. Per dimostrare questo teorema stabiliamo prima una disuguaglianza di tipo Moser–Trudinger per il problema lineare associato e concludiamo grazie ad un'applicazione di un metodo di punto fisso. 
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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/

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