Results on unique continuation for solutions to partial differential equations are of importance in many areas of applied mathematics, in particular in control theory and inverse problems. The unique continuation problem can be formulated as follows. Holmgren's theorem requires analytic coefficients of the differential operator. That makes it impractical for many applications. Its proof is based on a certain type of weighted energy estimate which was introduced by Carleman.
Applications often yield operators with time-independent coefficients.
In 1995, D. Tataru proved a sharp uniqueness result for equations with time independent coefficients using a new type of Carleman estimate. We will show that Tataru's result can be extended to some systems and higher order equations and present new uniqueness results for the Kirchhoff plate equation and a thermoelastic system. Marek Kimmel , of the Department of Statistics , Rice University . Microsatellite DNA is composed of tandem repeats of simple motifs of length 2-6 nucleotides. Because of its high mutation rate it provides a convenient tool for timing of evolutionary events on the time-scale on the order of 100,000 generations.