5 papers · 1 filter
Properties of the phase boundary in the parabolic problem with hysteresis
Darya Apushkinskaya, Sergey Tikhomirov, Nina Uraltseva
We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial…
Functional a posteriori error estimates for parabolic obstacle problems
Darya E. Apushkinskaya, Sergey I. Repin
The paper is concerned with functional type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce…
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
Darya E. Apushkinskaya, Sergey I. Repin
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the differenc…
Venttsel boundary value problems with discontinuous data
Darya E. Apushkinskaya, Alexander I. Nazarov, Dian K. Palagachev +1
We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maxim…
On the Boundary Point Principle for divergence-type equations
Darya E. Apushkinskaya, Alexander I. Nazarov
We provide some versions of the Zaremba-Hopf-Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coeffi…