The Cauchy problem for quasilinear SG‐hyperbolic systems |
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| Authors: | Marco Cappiello Luisa Zanghirati |
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| Institution: | 1. Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy;2. Phone: +39 0532 974004, Fax: +39 0532 247292;3. Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100, Ferrara, ItalyPhone: +39 0532 974034, Fax: +39 0532 247292 |
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| Abstract: | We study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on (t, x) ∈ 0, T ] × ?n and presenting a linear growth for |x | → ∞. We prove well‐posedness in the Schwartz space ?? (?n ). The result is obtained by deriving an energy estimate for the solution of the linearized problem in some weighted Sobolev spaces and applying a fixed point argument. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Cauchy problem quasilinear hyperbolic systems SG‐pseudo‐differential operators |
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