Displaying similar documents to “Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation”

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.

A sharp weighted Wirtinger inequality

Tonia Ricciardi (2005)

Bollettino dell'Unione Matematica Italiana

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We obtain a sharp estimate for the best constant C > 0 in the Wirtinger type inequality ∫ 0 2 ⁢ π γ p ⁢ ω 2 ≤ C ⁢ ∫ 0 2 ⁢ π γ q ⁢ ω ′ 2 where γ is bounded above and below away from zero, w is 2 ⁢ π -periodic and such that ∫ 0 2 ⁢ π γ p ⁢ ω = 0 , and p + q ≥ 0 . Our result generalizes an inequality of Piccinini and Spagnolo.

Classification of initial data for the Riccati equation

N. Chernyavskaya, L. Shuster (2002)

Bollettino dell'Unione Matematica Italiana

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We consider a Cauchy problem y ′ ⁢ x + y 2 ⁢ x = q ⁢ x , y ⁢ x x = x 0 = y 0 where x 0 , y 0 ∈ R and q ⁢ x ∈ L 1 loc ⁢ R is a non-negative function satisfying the condition: ∫ - ∞ x q ⁢ t ⁢ d ⁢ t > 0 , ∫ x ∞ q ⁢ t ⁢ d ⁢ t > 0 ⁢  for  ⁢ x ∈ R . We obtain the conditions under which y ⁢ x can be continued to all of R . This depends on x 0 , y 0 and the properties of q ⁢ x .