595 research outputs found
Parabolic equations with dynamical boundary conditions and source terms on interfaces
We consider parabolic equations with mixed boundary conditions and domain
inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump
in the conormal derivative. Only minimal regularity assumptions on the domain
and the coefficients are imposed. It is shown that the corresponding linear
operator enjoys maximal parabolic regularity in a suitable -setting. The
linear results suffice to treat also the corresponding nondegenerate
quasilinear problems.Comment: 30 pages. Revised version. To appear in Annali di Matematica Pura ed
Applicat
Optimal control solution for Pennes' equation using strongly continuous semigroup
summary:A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction and dissipative system. Mild solution for bioheat transfer equation and its adjoint problem are proposed. Controllability and exponentially stability for the related system is proved. The optimal control problem is solved using strongly continuous semigroup solution and time discretization. Mathematical simulations for a thermal therapy in the presence of point heating power are presented to investigate efficiency of the proposed technique
semigroup generation for Fokker-Planck operators associated with general L\'evy driven SDEs
We prove a new generation result in for a large class of non-local
operators with non-degenerate local terms. This class contains the operators
appearing in Fokker-Planck or Kolmogorov forward equations associated with
L\'evy driven SDEs, i.e. the adjoint operators of the infinitesimal generators
of these SDEs. As a byproduct, we also obtain a new elliptic regularity result
of independent interest. The main novelty in this paper is that we can consider
very general L\'evy operators, including state-space depending coefficients
with linear growth and general L\'evy measures which can be singular and have
fat tails
On the quantum description of Einstein's Brownian motion
A fully quantum treatment of Einstein's Brownian motion is given, showing in
particular the role played by the two original requirements of translational
invariance and connection between dynamics of the Brownian particle and atomic
nature of the medium. The former leads to a clearcut relationship with Holevo's
result on translation-covariant quantum-dynamical semigroups, the latter to a
formulation of the fluctuation-dissipation theorem in terms of the dynamic
structure factor, a two-point correlation function introduced in seminal work
by van Hove, directly related to density fluctuations in the medium and
therefore to its atomistic, discrete nature. A microphysical expression for the
generally temperature dependent friction coefficient is given in terms of the
dynamic structure factor and of the interaction potential describing the single
collisions. A comparison with the Caldeira Leggett model is drawn, especially
in view of the requirement of translational invariance, further characterizing
general structures of reduced dynamics arising in the presence of symmetry
under translations.Comment: 14 pages, latex, no figure
Stochastic evolution equations driven by Liouville fractional Brownian motion
Let H be a Hilbert space and E a Banach space. We set up a theory of
stochastic integration of L(H,E)-valued functions with respect to H-cylindrical
Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in
the interval (0,1). For Hurst parameters in (0,1/2) we show that a function
F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical
Liouville fBm if and only if it is stochastically integrable with respect to an
H-cylindrical fBm with the same Hurst parameter. As an application we show that
second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by
space-time noise which is white in space and Liouville fractional in time with
Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous
both and space.Comment: To appear in Czech. Math.
Dephasing-induced diffusive transport in anisotropic Heisenberg model
We study transport properties of anisotropic Heisenberg model in a disordered
magnetic field experiencing dephasing due to external degrees of freedom. In
the absence of dephasing the model can display, depending on parameter values,
the whole range of possible transport regimes: ideal ballistic conduction,
diffusive, or ideal insulating behavior. We show that the presence of dephasing
induces normal diffusive transport in a wide range of parameters. We also
analyze the dependence of spin conductivity on the dephasing strength. In
addition, by analyzing the decay of spin-spin correlation function we discover
a presence of long-range order for finite chain sizes. All our results for a
one-dimensional spin chain at infinite temperature can be equivalently
rephrased for strongly-interacting disordered spinless fermions.Comment: 15 pages, 9 PS figure
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