Abstract
We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wave evolution along the cylinder and prove estimates of the functional calculi of these first order non-self adjoint differential operators with non-smooth coefficients. Applying our new functional calculus, we obtain a one-to-one correspondence between polynomially bounded time-harmonic waves and functions in appropriate spectral subspaces.
Highlights
A linear partial differential equation, PDE, or a system of PDEs, is often analyzed by studying the evolution of solutions u with respect to one of the variables, say t
T, an infinitesimal generator, is a differential operator acting in the remaining variables x only, for each fixed t
The aim of the present paper is to study infinitesimal generators T arising as above in the elliptic case
Summary
A linear partial differential equation, PDE, or a system of PDEs, is often analyzed by studying the evolution of solutions u with respect to one of the variables, say t. Recall that if the PDE is of second or higher order, we can rewrite it as a system of first order equations, so without loss of generality we can assume that the PDE only contains first order derivatives in t. In this way the PDE becomes a vector-valued ordinary differential equation, ODE, like.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
