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Lutsky, Ya.; Rabinovich, V. S.

Invertibility of parabolic pseudodifferential operators with rapidly increasing symbols. (English) Zbl 1181.35356

Russ. J. Math. Phys. 15, No. 2, 267-279 (2008).
Summary: We consider pseudodifferential operators with rapidly increasing double symbols analytic with respect to the variable dual to the time on the lower complex half-plane. We construct invertibility theory for these operators in weighted Sobolev spaces with weights related to growths of symbols and give applications to heat equations with potentials of power, exponential, and superexponential growths.

Cited in 1 Document

MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
47G30 Pseudodifferential operators
35K05 Heat equation
35B40 Asymptotic behavior of solutions to PDEs

Keywords:

parabolic pseudodifferential operators; double symbols; invertibility; heat equation
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References:

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