Self-similar Asymptotic Profile for a Damped Evolution Equation
In this note, we describe the self-similar asymptotic profile for evolution equations with strong, effective damping. We assume that initial data are in weighted Sobolev spaces, and the second data verifies suitable moment conditions. The asymptotic profile is obtained by means of the application of a differential operator given by a linear combination of Riesz potentials to the fundamental solution of a (polyharmonic) diffusive problem.
The author has been supported by the INdAM—GNAMPA Project 2017 Equazioni di tipo dispersivo e proprietà asintotiche.
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