The Cauchy problem for quasilinear SG‐hyperbolic systems | Zendy

Cappiello Marco | Zendy; Zanghirati Luisa | Zendy

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The Cauchy problem for quasilinear SG‐hyperbolic systems

Author(s) -

Cappiello Marco,

Zanghirati Luisa

Publication year - 2007

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410511

Subject(s) - mathematics , sobolev space , initial value problem , cauchy problem , class (philosophy) , space (punctuation) , pure mathematics , mathematical analysis , argument (complex analysis) , cauchy distribution , hyperbolic partial differential equation , partial differential equation , linguistics , philosophy , biochemistry , chemistry , artificial intelligence , computer science

We study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on ( t , x ) ∈ [0, T ] × ℝ n and presenting a linear growth for | x | → ∞. We prove well‐posedness in the Schwartz space (ℝ 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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