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Displaying similar documents to “Some results on the well-posedness for systems with time dependent coefficients”

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

Amel Atallah Baraket (2004)

Bollettino dell'Unione Matematica Italiana

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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.