scholarly journals Large time behaviour for the heat equation on Z, moments and decay rates

2021 ◽  
Vol 500 (2) ◽  
pp. 125137
Author(s):  
Luciano Abadias ◽  
Jorge González-Camus ◽  
Pedro J. Miana ◽  
Juan C. Pozo
Keyword(s):  
Heat Equation ◽  
Large Time ◽  
Decay Rates ◽  
Time Behaviour ◽  
Large Time Behaviour

Regularity and large time behaviour of solutions of a conservation law without convexity

1985 ◽  
Vol 99 (3-4) ◽  
pp. 201-239 ◽  
Author(s):  
C. M. Dafermos
Keyword(s):  
Initial Data ◽  
Conservation Law ◽  
Large Time ◽  
Decay Rates ◽  
Time Behaviour ◽  
Large Time Behaviour ◽  
Jump Discontinuities ◽  
Contact Discontinuities ◽  
Finite Set ◽  
Line Characteristic

SynopsisUsing the method of generalized characteristics, we discuss the regularity and large time behaviour of admissible weak solutions of a single conservation law, in one space variable, with one inflection point.We show that when the initial data are C∞ then, generically, the solution is C∞ except: (a) on a finite set of C∞ arcs across which it experiences jump discontinuities (genuine shocks or left contact discontinuities); (b) on a finite set of straight line characteristic segments across which its derivatives of order m, m = 1, 2,…, experience jump discontinuities (weak waves of order m); and (c) on the finite set of points of interaction of shocks and weak waves. Weak waves of order 1 are triggered by rays grazing upon contact discontinuities. Weak waves of order m, m ≥ 2, are generated by the collision of a weak wave of order m − 1 with a left contact discontinuity.We establish sharp decay rates for solutions with initial data of the following types: (a) with bounded primitive; (b) with primitive having sublinear growth; (c) in L1; (d) of compact support; and (e) periodic.

Decay rates for the solutions of model equations for bore propagation

1995 ◽  
Vol 125 (2) ◽  
pp. 371-398 ◽  
Author(s):  
S. V. Rajopadhye
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Burgers Equation ◽  
Decay Rates ◽  
Time Behaviour ◽  
Large Time Behaviour ◽  
Temporal Decay ◽  
De Vries ◽  
Model Equations

We study the large-time behaviour of solutions to the Korteweg-de Vries-Burgers equation with bore-like initial data. This work relies on the methods of Amick, Bona and Schonbeck to obtain sharp rates of temporal decay of certain norms of the solution, thus obtaining an improvement over results of Naumkin and Shishmarev.

Large time behaviour of solutions for the heat equation with spatio-temporal delay

Nonlinearity ◽  
2008 ◽  
Vol 21 (4) ◽  
pp. 823-840 ◽  
Author(s):  
Chunhua Jin ◽  
Jingxue Yin ◽  
Chunpeng Wang
Keyword(s):  
Heat Equation ◽  
Large Time ◽  
Temporal Delay ◽  
Time Behaviour ◽  
Large Time Behaviour ◽  
Spatio Temporal

scholarly journals Large time behaviour of someN-body systems

1985 ◽  
Vol 101 (1) ◽  
pp. 129-152
Author(s):  
M. Krishna
Keyword(s):  
Large Time ◽  
Time Behaviour ◽  
Large Time Behaviour

Large time behaviour of solutions to the 3D-NSE in Xσ spaces

2020 ◽  
Vol 482 (2) ◽  
pp. 123566 ◽  
Author(s):  
Jamel Benameur ◽  
Mariem Bennaceur
Keyword(s):  
Large Time ◽  
Time Behaviour ◽  
Large Time Behaviour
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