On the decay properties of solutions to a class of Schrödinger equations

Authors:
L. Dawson, H. McGahagan and G. Ponce

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2081-2090

MSC (2000):
Primary 35J10; Secondary 35B65

DOI:
https://doi.org/10.1090/S0002-9939-08-09355-6

Published electronically:
February 14, 2008

MathSciNet review:
2383514

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrödinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate involving the projections onto the positive and negative frequencies.

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Additional Information

**L. Dawson**

Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089

Email:
ldawson@math.arizona.edu

**H. McGahagan**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
helena@math.ucsb.edu

**G. Ponce**

Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106

Email:
ponce@math.ucsb.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09355-6

Received by editor(s):
March 6, 2007

Published electronically:
February 14, 2008

Additional Notes:
The first author was supported by NSF grants

The second author was supported by an NSF postdoctoral fellowship

The third author was supported by NSF grants

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2008
American Mathematical Society