A degenerate hyperbolic equation under Levi conditions |
| |
Authors: | Alessia Ascanelli |
| |
Institution: | (1) Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy, Tel.: 0532/974004, Fax: 0532/247292, |
| |
Abstract: | Abstract We consider the Cauchy problem for a second order equation of hyperbolic type. This equation degenerates in two different
ways. On one hand, the coefficients have a bad behavior with respect to time: there is a blow-up phenomenon in the first time
derivative of the principal part’s coefficients, that is the derivative vanishes at the time t=0. On the other hand, the equation is weakly hyperbolic and the multiplicity of the roots is not constant, but zeroes are
of finite order.
Here we overcome the blow-up problem and, moreover, the finitely degeneration of the Cauchy problem allows us to give an appropriate
Levi condition on the lower order terms in order to get C∞ well posedness of the Cauchy problem.
Keywords: Cauchy problem, Hyperbolic equations, Levi conditions |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|