On the breakdown of solutions to N×N quasilinear hyperbolic systems

✍ Scribed by Renato Manfrin

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 272 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00101-3

✦ Synopsis

We shall be concerned with the development of singularities of the C 1 -solutions of the quasilinear N ×N hyperbolic system Ut +A(U )Ux =0 in one space dimension. Generalizing a nonlinearity condition introduced by MacCamy and Mizel (Arch. Rat. Mech. Anal. 25 (1967) 299-320), in this paper we prove some results of blow-up for the ÿrst-order derivatives without restrictions on the size of the initial data.