On the inverse of parabolic boundary value problems for large times

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We construct algebras of Volterra pseudodifferential operators that contain, in particular, the inverses of the most natural classical systems of parabolic boundary value problems of general form. Parabolicity is determined by the invertibility of the principal symbols, and as a result, is equivalent to the invertibility of the operators within the calculus. Existence, uniqueness, regularity, and asymptotics of solutions as t → ∞ are consequences of the mapping properties of the operators in exponentially weighted Sobolev spaces and subspaces with asymptotics. An important aspect of this work is that the microlocal and global kernel structure of the inverse operator (solution operator) of a parabolic boundary value problem for large times is clarified. Moreover, our approach naturally yields qualitative perturbation results for the solvability theory of parabolic boundary value problems. To achieve these results, we assign to t = ∞ the meaning of a conical point and treat the operators as totally characteristic pseudodifferential boundary value problems.

Original languageEnglish (US)
Pages (from-to)91-163
Number of pages73
JournalJapanese Journal of Mathematics
Volume30
Issue number1
DOIs
StatePublished - Jan 1 2004

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Boundary Value Problem
Operator
Invertibility
Volterra Operator
Existence-uniqueness
Weighted Sobolev Spaces
Regularity of Solutions
Uniqueness of Solutions
Asymptotics of Solutions
Pseudodifferential Operators
Assign
Solvability
Existence of Solutions
Calculus
Subspace
kernel
Perturbation
Algebra

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On the inverse of parabolic boundary value problems for large times. / Krainer, Thomas.

In: Japanese Journal of Mathematics, Vol. 30, No. 1, 01.01.2004, p. 91-163.

Research output: Contribution to journalArticle

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