We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, on R^3, the validity of such an expansion is established even with \ill-prepared" Cauchy data, by including an additional initial layer correction.
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Nanoscale pattern formation produced by ion bombardment of a rotating target: The decisive role of the ion energy
- Award ID(s):
- 2116753
- PAR ID:
- 10475849
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review E
- Volume:
- 107
- Issue:
- 1
- ISSN:
- 2470-0045
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion $$ m_e/M_i\ll 1$$ is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, on $$ \mathbb{R}^3$$, the validity of such an expansion is established even with ``ill-prepared'' Cauchy data, by including an additional initial layer correction.more » « less
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