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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Florent Berthelin, François Bouchut (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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 , 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.
Tonia Ricciardi (2005)
Bollettino dell'Unione Matematica Italiana
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We obtain a sharp estimate for the best constant in the Wirtinger type inequality where is bounded above and below away from zero, is -periodic and such that , and . Our result generalizes an inequality of Piccinini and Spagnolo.
N. Chernyavskaya, L. Shuster (2002)
Bollettino dell'Unione Matematica Italiana
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We consider a Cauchy problem where , and is a non-negative function satisfying the condition: We obtain the conditions under which can be continued to all of . This depends on , and the properties of .
Marina Ghisi (2001)
Rendiconti del Seminario Matematico della Università di Padova
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