31 citations · 137 across the 73 of their papers we have counts for
8 papers · 1 filter
Regularity of complexified hyperbolic equations with integral conditions
Nikolai Dokuchaev
This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achiev…
On recovering parabolic diffusions from their time-averages
Nikolai Dokuchaev
The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boun…
On prescribed change of profile for solutions of parabolic equations
Nikolai Dokuchaev
Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fi…
Universal estimates for parabolic equations and applications for non-linear and non-local problems
Nikolai Dokuchaev
We obtain some "universal" estimates for -norm of the solution of a parabolic equation via a weighted version of -norm of the free term. More precisely, we found the l…
Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion
Nikolai Dokuchaev
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in…
Universal estimate of the gradient for parabolic equations
Nikolai Dokuchaev
We suggest a modification of the estimate for weighted Sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the…