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Local existence and estimations for a semilinear wave equation in two dimension space

Amel Atallah Baraket — 2004

Bollettino dell'Unione Matematica Italiana

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 $L^{2} (R^{2})$ , 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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