4 citations · 6 across the 6 of their papers we have counts for
6 papers
On a Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a nonhomogeneous condition on an arc
Murdhy Aldawsari, Tatiana Savina
According to the Schwarz symmetry principle, every harmonic function vanishing on a real analytic curve has an odd continuation, while a harmonic function satisfying homogeneous Ne…
From reflections to elliptic growth
Tatiana Savina
We use reflections involving analytic Dirichlet and Neumann data on a real-analytic curve in order to find a representation of solutions to Cauchy problems for harmonic functions i…
On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources
T. V. Savina, L. Akinyemi, A. Savin
A two-phase Hele-Show problem with a time-dependent gap describes the evolution of the interface, which separates two fluids sandwiched between two plates. The fluids have differen…
Exact solutions to a Muskat problem with line distributions of sinks and sources
L. Akinyemi, T. V. Savina, A. A. Nepomnyashchy
The evolution of a two-phase Hele-Shaw problem, a Muskat problem, under assumption of a negligible surface tension is considered. We use the Schwarz function approach and allow the…
On non-local reflection for elliptic equations of the second order in R^2 (the Dirichlet condition)
Tatiana Savina
Point-to-point reflection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more…
On the dependence of the reflection operator on boundary conditions for biharmonic functions
Tatiana Savina
The biharmonic equation arises in areas of continuum mechanics including linear elasticity theory and the Stokes flows, as well as in a radar imaging problem. We discuss the reflec…