Evolution Equations and Control Theory, Partial Differential Equations and Mathematical Physics
I graduated from the University of Bucharest in 1989 and I obtained the PhD at the University Paris 7 in October 1994. In my thesis I introduced a new, geometric method for proving the unique continuation property. It avoids the use of Carleman estimates, which have been shown unable to give optimal results per se, and generalizes in some sense the logarithmic convexity approach.
In my subsequent work on unique continuation I obtained only counterexamples.
While I was visiting the Department of Mathematics of Bristol University (May 1997-June 1999), I become interested in estimates for the heat kernel and estimates of the low eigenvalues for planar domains.
I am currently visiting the Loughborough University where I am working on inverse problems with prof. Y.V.Kurylev and their numerical treatment with dr. K. Peat
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3DE, United Kingdom.
Permanent address
Institute of Mathematics of the Romanian Academy, Bucuresti, P.O. Box 1-764, RO-70700, ROMANIA.
- A Paley Wiener Theorem and Pseudolocal Operators, Revue Roumaine de Mathematiques pures et Appliquees, 35 (1990), 321-328.
- On $c_0$-groups in Hilbert space, Comptes Rendus de l'Academie de Sciences de Paris, serie I, vol.316 (1993), 873-878.
- Some remarks on unique continuation for Dirac operator, Letters in Mathematical Physics, 31 (1994), 85-93.
- Hilbert Space Estimates and Applications to Unique Continuation, doctoral dissertation, defended October 7, 1994 at the University Paris 7.
- On a counterexample concerning unique continuation for elliptic equations in divergence form, Mathematical Physics, Analysis, Geometry, 1998.
- On the computational power of context-free PC grammar systems , Theoretical Computer Science, (2000).
- Exponential clustering of eigenvalues for a big perturbation of the two-sphere , preprint IMAR, Nr 12/1998.
- A counterexample to unique continuation in dimension 2 , to appear in Communications in Analysis and Geometry.
Niculae.Mandache@imar.ro