On a weakly hyperbolic equation with a term of order zero. (English) Zbl 0895.35057

Summary: We study a weakly hyperbolic equation of second order, supposing that the coefficients of the principal part are analytic and depend only on time. We prove that if we add a term of order zero \(c(t,x)u\), with \(c\in C(\mathbb{R}^{n+1})\), the Cauchy problem remains well-posed in \(C^\infty\).


35L15 Initial value problems for second-order hyperbolic equations
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