It is well known that, in the presence of an attractive force having a Coulomb singularity, scattering solutions of the nonrelativistic \ALD equation having nonrunaway character do not exist, for the case of motions on the line. By numerical computations on the full three dimensional case, we give indications that indeed there exists a full tube of initial data for which nonrunay solutions of scatterig type do not exist. We also give a heuristic argument which allows to estimate the size of such a tube of initial data. The numerical computations also show that in a thin region beyond such a tube one has the nonuniqueness phenomenon, i.e. the ``mechanical'' data of position and velocity do not uniquely determine the nonrunaway trajectory.

On the existence of scattering solutions for the Abraham-Lorentz-Dirac equation / A. Carati. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 6:3(2006), pp. 471-480. [10.3934/dcdsb.2006.6.471]

On the existence of scattering solutions for the Abraham-Lorentz-Dirac equation

A. Carati
Primo
2006

Abstract

It is well known that, in the presence of an attractive force having a Coulomb singularity, scattering solutions of the nonrelativistic \ALD equation having nonrunaway character do not exist, for the case of motions on the line. By numerical computations on the full three dimensional case, we give indications that indeed there exists a full tube of initial data for which nonrunay solutions of scatterig type do not exist. We also give a heuristic argument which allows to estimate the size of such a tube of initial data. The numerical computations also show that in a thin region beyond such a tube one has the nonuniqueness phenomenon, i.e. the ``mechanical'' data of position and velocity do not uniquely determine the nonrunaway trajectory.
Scattering solutions, Abraham-Lorentz-Dirac equation
Settore MAT/07 - Fisica Matematica
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/12531
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact