Displaying similar documents to “Well posedness under Levi conditions for a degenerate second order Cauchy problem”

Some results on the well-posedness for systems with time dependent coefficients

Marcello D’Abbicco, Giovanni Taglialatela (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider hyperbolic systems with time dependent coefficients and size  2 or  3 . We give some sufficient conditions in order the Cauchy Problem to be well-posed in 𝒞 ∞ and in Gevrey spaces.

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.