scholarly journals Asymptotic behavior in time periodic parabolic problems with unbounded coefficients

2010 ◽  
Vol 249 (12) ◽  
pp. 3377-3418 ◽  
Author(s):  
Luca Lorenzi ◽  
Alessandra Lunardi ◽  
Alessandro Zamboni
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Problems ◽  
Unbounded Coefficients ◽  
Time Periodic

scholarly journals Asymptotic Behavior of Solutions of Parabolic Equations with Unbounded Coefficients

1970 ◽  
Vol 37 ◽  
pp. 5-12 ◽  
Author(s):  
Tadashi Kuroda
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Parabolic Equations ◽  
Half Line ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Unbounded Coefficients ◽  
The Real

Let Rn be the n-dimensional Euclidean space, each point of which is denoted by its coordinate x = (x1,...,xn). The variable t is in the real half line [0, ∞).

scholarly journals Mourre theory for time-periodic systems

1998 ◽  
Vol 149 ◽  
pp. 193-210 ◽  
Author(s):  
Koichiro Yokoyama
Keyword(s):  
Asymptotic Behavior ◽  
Adjoint Operator ◽  
The Self ◽  
Periodic Systems ◽  
Great Progress ◽  
Time Periodic ◽  
Commutator Method

Abstract.Studies for A.C. Stark Hamiltonian are closely related to that for the self-adjoint operator on torus. In this paper we use Mourre’s commutator method, which makes great progress for the study of time-independent Hamiltonian. By use of it we show the asymptotic behavior of the unitary propagator as σ → ± ∞.

ASYMPTOTIC BEHAVIOR OF SPATIALLY INHOMOGENEOUS BALANCE LAWS

2005 ◽  
Vol 02 (03) ◽  
pp. 645-672 ◽  
Author(s):  
JULIA EHRT ◽  
JÖRG HÄRTERICH
Keyword(s):  
Asymptotic Behavior ◽  
Vector Field ◽  
Initial Data ◽  
Periodic Solutions ◽  
Balance Laws ◽  
Spatially Inhomogeneous ◽  
Periodic Initial Data ◽  
Left And Right ◽  
Longtime Behavior ◽  
Time Periodic

We study the longtime behavior of spatially inhomogeneous scalar balance laws with periodic initial data and a convex flux. Our main result states that for a large class of initial data the entropy solution will either converge uniformly to some steady state or to a discontinuous time-periodic solution. This extends results of Lyberopoulos, Sinestrari and Fan and Hale obtained in the spatially homogeneous case. The proof is based on the method of generalized characteristics together with ideas from dynamical systems theory. A major difficulty consists of finding the periodic solutions which determine the asymptotic behavior. To this end we introduce a new tool, the Rankine–Hugoniot vector field, which describes the motion of a (hypothetical) shock with certain prescribed left and right states. We then show the existence of periodic solutions of the Rankine–Hugoniot vector field and prove that the actual shock curves converge to these periodic solutions.

scholarly journals Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

2018 ◽  
Vol 24 (1) ◽  
pp. 105-127
Author(s):  
Fabio Punzo ◽  
Enrico Valdinoci
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Time Dependent ◽  
Uniqueness Of Solutions ◽  
Unbounded Coefficients ◽  
Conditions At Infinity

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.

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