Faculty Research Publications (Mathematics)http://hdl.handle.net/1957/138182014-08-31T06:39:13Z2014-08-31T06:39:13ZSkew Disperson and Continuity of Local Timehttp://hdl.handle.net/1957/517602014-08-29T19:24:52Z2014-07-01T00:00:00ZSkew Disperson and Continuity of Local Time
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain a characterization of large scale
parameters and behavior by an analysis at the fine scale of stochastic particle motions.
In particular, considering particle concentration modeled by a diffusion equation with
piecewise constant diffusion coefficient, it is shown that the continuity of a natural
modification of local time is the individual (stochastic) particle scale equivalent to continuity
of flux at the scale of the (macroscopic) particle concentrations. Consequences
of this involve the determination of a skewness transmission probability in the presence
of an interface, as well as corollaries concerning interfacial effects on occupation time
of the associated stochastic particles.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/10955.
2014-07-01T00:00:00ZTwo-scale convergence of a model for flow in a partially fissured mediumClark, G. W.Showalter, R. E.http://hdl.handle.net/1957/512302014-08-07T20:53:16Z1999-01-14T00:00:00ZTwo-scale convergence of a model for flow in a partially fissured medium
Clark, G. W.; Showalter, R. E.
The distributed-microstructure model for the flow of single phase
fluid in a partially fissured composite medium due to Douglas-Peszyńska-Showalter [12] is extended to a quasi-linear version. This model contains the
geometry of the local cells distributed throughout the medium, the flux exchange
across their intricate interface with the imbedded fissure system, and
the secondary flux resulting from diffusion paths within the matrix. Both the
exact but highly singular micro-model and the macro-model are shown to be
well-posed, and it is proved that the solution of the micro-model is two-scale
convergent to that of the macro-model as the spatial parameter goes to zero.
In the linear case, the effective coefficients are obtained by a partial decoupling
of the homogenized system.
This is the publisher’s final pdf. The published article is copyrighted by Texas State University and can be found at: http://www.emis.ams.org/journals/EJDE/index.html.
1999-01-14T00:00:00ZMultiscale elliptic-parabolic systems for flow and transportPeszyńska, MalgorzataShowalter, Ralph E.http://hdl.handle.net/1957/512262014-08-07T20:42:13Z2007-11-05T00:00:00ZMultiscale elliptic-parabolic systems for flow and transport
Peszyńska, Malgorzata; Showalter, Ralph E.
See article for Abstract.
This is the publisher’s final pdf. The published article is copyrighted by Texas State University and can be found at: http://ejde.math.txstate.edu/index.html.
2007-11-05T00:00:00ZNonlinear Degenerate Evolution Equations in Mixed FormulationShowalter, R. E.http://hdl.handle.net/1957/512242014-08-07T20:26:58Z2010-08-31T00:00:00ZNonlinear Degenerate Evolution Equations in Mixed Formulation
Showalter, R. E.
We develop the theory of degenerate and nonlinear evolution systems in mixed formulation.
It will be shown that many of the well-known results for the stationary problem extend to
the nonlinear case and that the dynamics of a degenerate Cauchy problem is governed by a nonlinear
semigroup. The results are illustrated by a Darcy–Stokes coupled system with multiple nonlinearities.
This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.
2010-08-31T00:00:00Z