14 citations · 24 across the 12 of their papers we have counts for
14 papers
Well-posedness results for hyperbolic operators with coefficients rapidly oscillating in time
Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli
In the present paper, we consider second order strictly hyperbolic linear operators of the form , for $(t,x)\in[0,T]\tim…
On some hyperbolic equations of third order
Ferruccio Colombini, Todor Gramchev, Nicola Orrù +1
We give sufficient conditions for the well-posedness in of the Cauchy problem for third order equations with time dependent coefficients.
No loss of derivatives for hyperbolic operators with Zygmund-continuous coefficients in time
Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli
In this note we prove a well-posedness result, without loss of derivatives, for strictly hyperbolic wave operators having coefficients which are Zygmund-continuous in the time vari…
A Discrete Algorithm for General Weakly Hyperbolic Systems
Ferruccio Colombini, Tatsuo Nishitani, Jeffrey Rauch
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for eac…
On the Cauchy problem for
Ferruccio Colombini, Tatsuo Nishitani
We consider the Cauchy problem for second order differential operators with two independent variables . Assume that is a nonnegative …
Weyl formula for the negative dissipative eigenvalues of Maxwell's equations
Ferruccio Colombini, Vesselin Petkov
Let be the semigroup generated by Maxwell's equations in an exterior domain with dissipative boundary condition $E_{tan}- γ(…
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli +1
The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuou…
Eigenvalues for Maxwell's equations with dissipative boundary conditions
Ferruccio Colombini, Vesselin Petkov, Jeffrey Rauch
Let be the semigroup generated by Maxwell's equations in an exterior domain with dissipative boundary condition $E_{tan}- γ(…
The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients
Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli +1
In this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just…
A well-posedness result for hyperbolic operators with Zygmund coefficients
Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli +1
In this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coefficients both in time and in space…
A note on non-homogeneous hyperbolic operators with low-regularity coefficients
Ferruccio Colombini, Francesco Fanelli
In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to…
Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients
Ferruccio Colombini, Daniele Del Santo, Francesco Fanelli +1
In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension . We will suppose the coefficients…
Spectral problems for non elliptic symmetric systems with dissipative boundary conditions
Ferruccio Colombini, Vesselin Petkov, Jeffrey Rauch
This paper considers and extends spectral and scattering theory to dissipative symmetric systems that may have zero speeds and in particular to strictly dissipative boundary condit…
Incoming and disappearing solutions for Maxwell's equations
Ferruccio Colombini, Vesselin Petkov, Jeffrey Rauch
We prove that in contrast to the free wave equation in there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We const…