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Geometric blow up of \(2\times 2\) quasilinear systems in one space dimension. (Chinese. English summary) Zbl 1064.35110

Summary: In order to study lifespan and blow up mechanism of the quasilinear hyperbolic system solution, S. Alinhac introduced the idea of “geometric blow up” for general quasilinear system and gives blowup system [Am. J. Math. 117, No. 4, 987–1017 (1995; Zbl 0840.35060); Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 22, No. 3, 493–515 (1995; Zbl 0840.35059)]. At the same time, he proved geometric blow up mechanism for \(2\times 2\) quasilinear homogeneous strictly hyperbolic systems in one space dimension. Under general condition, geometric blow up of the classical solution is proved in this paper by using some skill for \(2\times 2\) quasilinear nonhomogeneous strictly hyperbolic systems in one space dimension, and some results of S. Alinhac’s are extended.

MSC:

35L60 First-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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