The paper deals with the problem of the propagation of analytic regularity of the solutions to the weakly hyperbolic equations $\partial^m_tu+G(t,x,\partial^\alpha_{t,x}u)_{|\alpha|\leq m-1}=0$. The authors prove that the solution is analytic in every cylinder $[0,T]\times \omega$ if $G$ and the initial data are analytic, and the solution $u$ is assumed to be in some Gevrey class of order $\sigma_1$ smaller than $1/\rho$ with an index $\rho \leq 1-1/m$ which is determined by the derivatives of $u$ that appear in $G$.

Propagation of analytic and Gevrey regularity for a class of semi-linear weakly hyperbolic equations

ZANGHIRATI, Luisa
1995

Abstract

The paper deals with the problem of the propagation of analytic regularity of the solutions to the weakly hyperbolic equations $\partial^m_tu+G(t,x,\partial^\alpha_{t,x}u)_{|\alpha|\leq m-1}=0$. The authors prove that the solution is analytic in every cylinder $[0,T]\times \omega$ if $G$ and the initial data are analytic, and the solution $u$ is assumed to be in some Gevrey class of order $\sigma_1$ smaller than $1/\rho$ with an index $\rho \leq 1-1/m$ which is determined by the derivatives of $u$ that appear in $G$.
1995
Cicognani, M.; Zanghirati, Luisa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1211218
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