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Gevrey well-posedness for pseudosymmetric systems with lower order terms. (English) Zbl 1058.35144

Ancona, Vincenzo (ed.) et al., Hyperbolic differential operators and related problems. New York, NY: Marcel Dekker (ISBN 0-8247-0963-2/pbk). Lect. Notes Pure Appl. Math. 233, 67-81 (2003).
The authors deal with the Cauchy problem \[ \begin{gathered}\partial_t u= A(t)\partial_x u+ B(t)u\quad\text{on }[0,T]\times \mathbb{R}_x,\\ u|_{t=0}= u_0(x),\end{gathered} \] where \(B(t)\) is an arbitrary matrix with entries belonging to \(L^\infty(0,T)\). They prove the well-posedness in Gevrey classes \(\gamma^s\equiv \gamma^s(\mathbb{R}_x)\) for a suitable range of the Gevrey exponent. To this end the authors assume that \(A(t)\) is a pseudosymmetric matrix.
For the entire collection see [Zbl 1027.00009].

MSC:

35L40 First-order hyperbolic systems
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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