ON THE RECOVERY, FROM A COUNTABLE COLLECTION OF POLYNOMIAL CONSERVATION LAWS, OF ACTION VARIABLES FOR THE KdV EQUATION IN THE CLASS OF ALMOST PERIODIC FUNCTIONS

1987 ◽  
Vol 56 (2) ◽  
pp. 417-428 ◽  
Author(s):  
M V Novitskiĭ
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Countable Collection ◽  
The Kdv Equation ◽  
Action Variables

scholarly journals On the Cauchy problem for scalar conservation laws in the class of Besicovitch almost periodic functions: Global well-posedness and decay property

2016 ◽  
Vol 13 (03) ◽  
pp. 633-659 ◽  
Author(s):  
Evgeny Yu. Panov
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Almost Periodic Functions ◽  
Entropy Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Scalar Conservation Law ◽  
The Cauchy Problem ◽  
Scalar Conservation ◽  
Necessary And Sufficient

We study the Cauchy problem for a multidimensional scalar conservation law with merely continuous flux vector in the class of Besicovitch almost periodic functions. The existence and uniqueness of entropy solutions are established. We also uncover the necessary and sufficient condition for the decay of almost periodic entropy solutions as the time variable [Formula: see text]. Our results are then interpreted in the framework of conservation laws on the Bohr compact.

Almost periodic functions

Mathematika ◽  
1955 ◽  
Vol 2 (2) ◽  
pp. 128-131 ◽  
Author(s):  
J. D. Weston
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions

scholarly journals Almost periodic functions and hyperbolic counting

2018 ◽  
Vol 14 (09) ◽  
pp. 2343-2368
Author(s):  
Giacomo Cherubini
Keyword(s):  
Asymptotic Variance ◽  
Limiting Distribution ◽  
Almost Periodic Functions ◽  
Specific Class ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Circle Problem

We prove the existence of asymptotic moments and an estimate on the tails of the limiting distribution for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrated versions of the remainder, and were considered originally (with due adaptations to our settings) by Wolfe, Phillips and Rudnick, and Hill and Parnovski.

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