This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak solutions. In Menzala (2002) the case where solutions vanish on a neighborhood of both extremes of the bounded interval where equation holds was solved combining...
This work is devoted to prove the exponential decay for the energy
of solutions of the Korteweg-de Vries equation in a bounded interval
with a localized damping term. Following the method in Menzala (2002)
which combines energy estimates, multipliers and compactness
arguments the problem is reduced to prove the unique continuation of
weak solutions. In Menzala (2002) the case where solutions vanish on a
neighborhood of both extremes of the bounded interval where equation
holds was solved combining...
This work is devoted to the
analysis of a viscous finite-difference space semi-discretization
of a locally damped wave equation in a regular 2-D domain. The
damping term is supported in a suitable subset of the domain, so
that the energy of solutions of the damped continuous wave
equation decays exponentially to zero as time goes to infinity.
Using discrete multiplier techniques, we prove that adding a
suitable vanishing numerical viscosity term leads to a uniform
(with respect to the mesh size)...
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