Frank Jochmann
Asymptotic behaviour of solutions of semilinear hyperbolic systems in arbitrary domains

MSC:

35B40 Asymptotic behavior of solutions

35Q60 Equations of electromagnetic theory and optics

35L05 Wave equation

35L40 General theory of hyperbolic systems of first-order PDE

Abstract: In this paper the long time asymptotic behaviour of solutions to
semilnear first order hyperbolic systems including Maxwell's equations
and the scalar wave-equation in an arbitrary spatial domain
is investigated. Weak conergence to stationary states is proved.
The possibly nonlinear damping-term may vanish on some subdomain
and obeys on the other part of the domain a coerciveness condition,
but it is not necessarily monotone. In the case that it is monotone
also strong $L^q$-convergence is shown.