130 citations · 192 across the 13 of their papers we have counts for
15 papers
Holder regularity for nonlocal in time subdiffusion equations with general kernel
Adam Kubica, Katarzyna Ryszewska, Rico Zacher
We study the regularity of weak solutions to nonlocal in time subdiffusion equations for a wide class of weakly singular kernels appearing in the generalised fractional derivative…
Holder continuity of weak solutions to evolution equations with distributed order fractional time derivative
Adam Kubica, Katarzyna Ryszewska, Rico Zacher
We study the regularity of weak solutions to evolution equations with distributed order fractional time derivative. We prove a weak Harnack inequality for nonnegative weak supersol…
A self-similar solution to time-fractional Stefan problem
Adam Kubica, Katarzyna Ryszewska
We derive the fractional version of one-phase one-dimensional Stefan model. We assume that the diffusive flux is given by the time-fractional Riemann-Liouville derivative, i.e. we…
Global in time solution to Kolmogorov's two-equation model of turbulence with small initial data
Przemysław Kosewski, Adam Kubica
We prove the existence of global in time solution to Kolmogorov's two-equation model of turbulence in three dimensional domain with periodic boundary conditions under smallness ass…
A note about fractional Stefan problem
Adam Kubica, Katarzyna Ryszewska
We derive the fractional version of one-phase one-dimensional Stefan model. We assume that the diffusive flux is given by the time-fractional Riemann-Liouville derivative, i.e. we…
Local in time solution to Kolmogorov's two-equation model of turbulence
Przemysław Kosewski, Adam Kubica
We prove the existence of local in time solution to Kolmogorov's two-equation model of turbulence in three dimensional domain with periodic boundary conditions. We apply Galerkin m…
Decay of solutions to parabolic-type problem with distributed order Caputo derivative
Adam Kubica, Katarzyna Ryszewska
We consider the decay of solution to fractional diffusion equation with the distributed order Caputo derivative. We assume that the elliptic operator is time-dependent and that the…
Fractional diffusion equation with the distributed order Caputo derivative
Adam Kubica, Katarzyna Ryszewska
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator un…
Initial-boundary value problems for fractional diffusion equations with time-dependent coeffcients
Adam Kubica, Masahiro Yamamoto
We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time var…
Weak solutions of fractional differential equations in non cylindrical domain
Adam Kubica, Piotr Rybka, Katarzyna Ryszewska
We study a time fractional heat equation in a noncylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin…
Fine singularity analysis of solutions to the Laplace equation: Berg's effect
Adam Kubica, Piotr Rybka
We study Berg's effect on special domains. This effect is understood as monotonicity of a harmonic function (with respect to the distance from the center of a flat part of the boun…
Fine singularity analysis of solutions to Laplace equation
Adam Kubica, Piotr Rybka
We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann on one component of…
Regularity criteria of weak solutions to NSE in some bounded domains involving the pressure
Adam Kubica, Bernard Nowakowski, Wojciech ZajcAczkowski
We present a short and elegant proof of an estimate for the pressure in terms of the velocity and external data in bounded domains under the slip and Navier boundary conditions. We…
Remarks on Regularity Criteria for Axially Symmetric Weak Solutions to the Navier-Stokes Equations, II
Adam Kubica
We examine the conditional regularity of the solutions of Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We…
Remarks on Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier Stokes Equations
Adam Kubica
We show that if v is an axially symmetric suitable weak solution to the Navier Stokes equations (in the sense of L. Caffarelli, R. Kohn & L. Nirenberg) such that the radial compone…