Browsing Mathematics, Statistics, and Physics by Subject "Helmholtz equation"
Now showing items 14 of 4

The Carleman formula for the Hemholtz equation on the plane
(Springer Science+Business Media, Inc., 2006)We consider the Cauchy problem for the Helmholtz equation in an arbitrary bounded planar domain with Cauchy data only on part of the boundary of the domain. We derive a Carlemantype formula for a solution to this problem ... 
Increasing stability for near field from the scattering amplitude
(American Mathematical Society, 2015)We obtain stability estimates for the near field of a radiating solution of the Helmholtz equation from the far field (scattering amplitude). This estimates contain the best possible Lipschitz term, a Holder term, and terms ... 
On increasing stability of the continuation for elliptic equations of second order without (Pseudo)convexity assumptions
(American Institute of Mathematical Sciences, 201910)We derive bounds of solutions of the Cauchy problem for general elliptic partial differential equations of second order containing parameter (wave number) k which are getting nearly Lipschitz for large k. Proofs use energy ... 
On the inverse source problem with boundary data at many wave numbers
(Springer, 20200204)We review recent results on inverse source problems for the Helmholtz type equations from boundary measurements at multiple wave numbers combined with new results including uniqueness of obstacles. We consider general ...