The unique continuation property for second order evolution PDEs

Mourad Choulli ()
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Mourad Choulli: Université de Lorraine

Partial Differential Equations and Applications, 2021, vol. 2, issue 5, 1-46

Abstract: Abstract We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and Schödinger operators with time-independent principal part. Our method is builds on two-parameter Carleman inequalities combined with unique continuation across a pseudo-convex hypersurface with respect to the space variable. The most results we demonstrate in this work are more or less classical. Some of them are not stated exactly as in their original form.

Keywords: Wave equation; Parabolic equation; Schrödinger equation; Elliptic equation; Carleman inequality; Pseudo-convexity condition; Non characteristic hypersurface; Property of unique continuation; Observability inequality; 35A23; 35J15; 35K10; 35L10 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s42985-021-00123-6

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