scholarly journals Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data

2013 ◽  
Vol 93 ◽  
pp. 3-14 ◽  
Author(s):  
Toyohiko Aiki ◽  
Adrian Muntean
Keyword(s):  
Large Time ◽  
Time Dependent ◽  
Henry's Law ◽  
Large Time Asymptotics ◽  
Henry’S Law ◽  
Dirichlet Data ◽  
Time Asymptotics

scholarly journals Schrödinger evolution of superoscillations with $$\delta $$- and $$\delta '$$-potentials

2019 ◽  
Vol 7 (3) ◽  
pp. 293-305 ◽  
Author(s):  
Yakir Aharonov ◽  
Jussi Behrndt ◽  
Fabrizio Colombo ◽  
Peter Schlosser
Keyword(s):  
Entire Function ◽  
Initial Data ◽  
Plane Wave ◽  
Large Time ◽  
Main Tool ◽  
Time Dependent ◽  
Convolution Operators ◽  
Compact Sets ◽  
Large Time Asymptotics ◽  
Time Asymptotics

AbstractIn this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with $$\delta $$ δ - and $$\delta '$$ δ ′ -potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space $$A_1(\mathbb {C})$$ A 1 ( C ) . Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under $$\delta $$ δ - and $$\delta '$$ δ ′ -potentials.

What happens with the Ekman current under constant wind?

2021 ◽  
Author(s):  
Victor Shrira ◽  
Rema Almelah
Keyword(s):  
Wave Field ◽  
Large Time ◽  
Wind Waves ◽  
Time Dependent ◽  
Stokes Drift ◽  
Large Time Asymptotics ◽  
Time Asymptotics ◽  
Field Evolution ◽  
Self Similar ◽  
Ekman Current

<p>The work examines the Ekman current  response to a steady<br>wind within the Stokes-Ekman paradigm. Under constant wind<br>in the classical Ekman model there is a single attractor<br>corresponding to the Ekman (1905)steady solution. It is<br>known that the account of wind waves  strongly affects the<br>Ekman current dynamics via the Stokes drift, which is<br>described by the Stokes-Ekman  model. Waves continue to<br>evolve even under constant wind, which makes  steady<br>solutions of the Stokes-Ekman equation impossible. Since<br>the dynamics of the Ekman response in the presence of<br>evolving wave field have not been considered,  the basic<br>questions on how  the Ekman current evolves and,<br>especially, whether it grows or decays at large times,<br>remain open.</p><p>Here by employing the known self-similar laws of wave<br>field evolution and  solving analytically the<br>the Stokes-Ekman equation we  find and analyse<br>evolution of the Ekman current. We show that the system has<br>a single time dependent attractor which can be described<br>asymptotically. The large time asymptotics of the Ekman<br>current is found to be determined by the regime of wave<br>field evolution:  for the regimes typical of young waves<br> the Ekman current grows with time to infinity, in contrast, for<br>`old waves'  the Ekman current asymptotically decays.</p><p> </p>

SIMULATIONS OF THE LIFSHITZ–SLYOZOV EQUATIONS: THE ROLE OF COAGULATION TERMS IN THE ASYMPTOTIC BEHAVIOR

2013 ◽  
Vol 23 (07) ◽  
pp. 1177-1215 ◽  
Author(s):  
THIERRY GOUDON ◽  
FRÉDÉRIC LAGOUTIÈRE ◽  
LÉON MATAR TINE
Keyword(s):  
Asymptotic Behavior ◽  
Large Time ◽  
Finite Volume Schemes ◽  
Large Time Asymptotics ◽  
Asymptotic Profile ◽  
Time Asymptotics ◽  
Supersaturated Solid Solutions ◽  
Kinetics Of ◽  
Selection Of

We consider the Lifshitz–Slyozov system that describes the kinetics of precipitation from supersaturated solid solutions. We design specific Finite Volume schemes and we investigate numerically the behavior of the solutions, in particular the large time asymptotics. Our purpose is two-fold: first, we introduce an adapted scheme based on downwinding techniques in order to reduce the numerical diffusion; second, we discuss the influence of coagulation effects on the selection of the asymptotic profile.

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