1 - 10 of 22 articles
This paper studies the analyticity of the Stokes semigroup in an infinite cylinder or more generally a cylindrical domain with several exits to infinity in the space
-closure of all smooth compactly supported solenoidal vector...
In this paper, we establish optimal solvability results—maximal regularity theorems—for the Cauchy problem for linear parabolic differential equations of arbitrary order acting on sections of tensor bundles over boundaryless complete Riemannian manifolds
We prove existence and uniqueness of global solutions for a class of reaction–advection– anisotropic-diffusion systems whose reaction terms have a “triangular structure”. We thus extend previous results to the case of time–space-dependent anisotropic diffusions and with time–space-dependent...
Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier–Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the outlet. As a key building block for the analysis of such...
Motivated by recent applications of weighted norm inequalities to maximal regularity of first- and second-order Cauchy problems, we study real interpolation spaces on the basis of general Banach function spaces and, in particular, weighted rearrangement invariant Banach function spaces. We show...
We consider a reaction–diffusion equation perturbed by noise (not necessarily white). We prove an integral inequality for the invariant measure
of a stochastic reaction–diffusion equation. Then, we discuss some consequences as an integration by parts formula which extends to...
We consider the linear thermoelastic plate equations with free boundary conditions in the
in time and
in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform
We examine a stochastic integral equation driven by Poisson random measures. The increase or decrease of the regularity of the solution in space and time is examined as a function of the parameters of the kernels. The space regularity is measured in real interpolation spaces. The results...
We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal evolution model of cancer cell growth. This model has a...
For a Navier–Stokes–Nernst–Planck–Poisson system we construct global weak solutions in a three-dimensional bounded domain. A special feature of our approach is that we allow for nonconstant diffusion coefficients which may vary from species to species as well as for
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