Unique continuation property for multi-terms time fractional diffusion equations

Ching Lung Lin, Gen Nakamura

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper concens about a Carleman estimate which can give the unique continuation property of solutions for a multi-terms time fractional diffusion equation up to order α(0<α<2) with general time dependent second order strongly elliptic operator for the diffusion. By using a special Holmgren type transformation which is linear with respect to time, the estimate giving a local unique continuation of solutions is derived via some subelliptic estimate for an operator associated to this transformed equation using calculus of pseudo-differential operators. After that we have given a new argument to derive the global unique continuation of solutions. Here the global unique continuation means as follows. If u is a solution of the multi-terms time fractional diffusion equation in a domain over the time interval (0, T) and it is supported on t≥ 0 , then a zero set of solution over a subdomain of Ω can be continued to (0 , T) × Ω.

Original languageEnglish
Pages (from-to)929-952
Number of pages24
JournalMathematische Annalen
Volume373
Issue number3-4
DOIs
Publication statusPublished - 2019 Apr 1

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Unique Continuation
Fractional Diffusion Equation
Term
Carleman Estimate
Zero set
Pseudodifferential Operators
Elliptic Operator
Estimate
Calculus
Interval
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Unique continuation property for multi-terms time fractional diffusion equations. / Lin, Ching Lung; Nakamura, Gen.

In: Mathematische Annalen, Vol. 373, No. 3-4, 01.04.2019, p. 929-952.

Research output: Contribution to journalArticle

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