## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
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- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
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EECT

The convergence is established for a sequence of operator semigroups, where the limiting object is the transition semigroup for a reflected stable processes. For semilinear equations involving the generators of these transition semigroups, an approximation method is developed as well. This makes it possible to derive an

*a priori*bound for solutions to these equations, and therefore prove global existence of solutions. An application to epidemiology is also given.
EECT

We consider an optimal control problem involving the use of
bacteria for pollution removal where the model assumes the bacteria
switch instantaneously between active and dormant states, determined
by threshold sensitivity to the local concentration $v$ of a diffusing
critical nutrient; compare [7], [3], [6] in which
nutrient transport is convective. It is shown that the direct problem
has a solution for each boundary control $ψ = ∂v/∂n$ and that
optimal controls exist, minimizing a combination of residual pollutant
and aggregated cost of the nutrient.

DCDS-S

For a chemical reaction/diffusion system, a very fast reaction $A+B\to C$
implies non-coexistence of $A,B$ with resulting interfaces. We try to understand
how these interfaces evolve in time. In particular, we seek a characterizing system
of equations and conditions for the sharp interface limit: when this fast reaction
is taken as infinitely fast.

keywords:
Asymptotic dynamics
,
Thiele modulus
,
Interface conditions.
,
System
,
Reaction-diffusion
,
Fast reaction

DCDS

We assume, for a distributed parameter control system, that a
linear stabilizing is available. We then seek a stabilizing,
necessarily nonlinear, subject to an

*a priori*bound on the control.
DCDS-B

Suggested by conversations in 1991 (Mark Krasnosel'skiĭ and Aleksei Pokrovskiĭ with TIS), this paper generalizes earlier work [7] of theirs
by defining a setting of hybrid systems with isotone switching rules
for a partially ordered set of modes and then obtaining a periodicity
result in that context. An application is given to a partial
differential equation modeling calcium release and diffusion in
cardiac cells.

keywords:
fixed point
,
isotone
,
Periodic
,
discontinuous
,
hybrid system
,
calcium waves.
,
hysteresis

## Year of publication

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