**abstract:**
In the hyperbolic Cauchy problem, the well-posedness in Sobolev spaces and the modulus of continuity of the coefficients are deeply connected.
This holds true in the more general framework of evolution equations with real characteristics
\[D_t^2u-\sum_{k=0}^{2p}a_k(t,x)D_x^ku=0\]
(\(p=1\) hyperbolic equations, \(p=2\) vibrating beam models,...) where a sharp scale of Hoelder continuity, with respect
to the time variable \(t\), for the \(a_k\)'s has been
established.

We show that, for \(p\geq2\), a lack of regularity in \(t\) can be compensated by a decay as the space variable \(x\to\infty\). This is not true in the hyperbolic case \(p=1\) because of the finite speed of propagation.

Thu 4 Jul, 15:00 - 15:50, Aula Dini

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