1,721,144 research outputs found
Some inverse problems of identification for integrodifferential parabolic systems with a boundary memory term
No full textWe discuss two inverse problems of reconstruction of data in a mixed parabolic integrodifferential problem. First, we shall consider the reconstruction on a factor depending on time in the source term. Next, we shall consider the reconstruction of a convolution kerne
Classical solutions to quasilinear parabolic problems with dynamic boundary conditions
No full textWe study linear nonautonomous parabolic systems with dynamic
boundary conditions. Next, we apply these results to show a theorem of local
existence and uniqueness of a classical solution to a second order quasilinear
system with nonlinear dynamic boundary conditions
Reconstruction of a convolution kernel in an integrodifferential problem with a fractional time derivative
Full text linkWe consider the problem of reconstruction of a convolution kernel (together with the solution) for a linear abstract evolution equation with a fractional time derivative
Parabolic problems with general Wentzell boundary conditions and diffusion on the boundary
No full textWe show a result of maximal regularity in spaces of H ̈older continuous
function, concerning linear parabolic systems, with dynamic or Wentzell
boundary conditions, with an elliptic di↵usion term on the boundary
Abstract elliptic problems depending on a parameter and parabolic problems with dynamic boundary conditions
No full textWe study abstract elliptic problems depending on a complex parameter. Such parameter appears also in the boundary conditions. Next, we consider abstract parabolic systems with dynamic boundary conditions. Applications are given to parameter elliptic boundary value problems and to concrete parabolic problems
Linear parabolic problems with dynamic boundary conditions in spaces of Hölder continuous functions
No full textWe consider a mixed linear parabolic problem with a second-order strongly elliptic
operator and with dynamic boundary conditions, in a domain with smooth boundary Ω. For
each β ∈ (0, 1), we determine necessary and sufficient assumptions on the data, so that there
exist a unique solution u in C1+β/2,2+β((0, T )×Ω), with Dtu|(0,T )×∂Ω bounded with values
in C1+β(∂Ω)
On Reconstruction of a Source Term Depending on Time and Space Variables in a Parabolic Mixed Problem
No full textWe determine a factor depending on both time and one of the
spaces variables in a mixed parabolic system in a cylindrical domain.
In order to do this, we employ a certain supplementary information,
concerning a space-time measurement of the solution
Preface [Special issue on mathematical models and analytical problems in modern continuum thermomechanics dedicated to Mauro Fabrizio]
No full textReconstruction of kernel depending also on space variable
No full textThe paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic type. This problem describes uniaxial deformations u of a cylindrical domain (0, π)×Ω, which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on Ω-sections perpendicular to the x axis. Various types of boundary conditions in [0, T ] × {0, π} × Ω are prescribed, whereas Dirichlet conditions are assumed in [0, T ] × (0, π) × ∂Ω. In order to reconstruct both u and k we suppose of knowing for any time t and any x ∈ (0, π) the flux of the viscoelastic stress vector through the boundary of the Ω-section. The main novelty is that the unknown kernel k is allowed to depend, not only on the time variable t, but also on the space variable x
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