Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation

João-Paulo Dias; Mário Figueira

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

Solution with finite energy to a BGK system relaxing to isentropic gas dynamics

Florent Berthelin, François Bouchut (2000)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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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

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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 $\int_{0}^{2 π} γ^{p} ω^{2} \leq C \int_{0}^{2 π} γ^{q} ω^{'}^{2}$ where $γ$ is bounded above and below away from zero, $w$ is $2 π$ -periodic and such that $\int_{0}^{2 π} γ^{p} ω = 0$ , and $p + q \geq 0$ . 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 $x_{0}$ , $y_{0} \in R$ and $q (x) \in L_{1}^{loc} (R)$ is a non-negative function satisfying the condition: $\int_{- \infty}^{x} q (t) d t > 0, \int_{x}^{\infty} q (t) d t > 0 for x \in R .$ 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 $q (x)$ .

Some remarks on global solutions to nonlinear dissipative mildly degenerate Kirchhoff strings

Marina Ghisi (2001)

Rendiconti del Seminario Matematico della Università di Padova

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