The law of the iterated logarithm for the solution of the Burgers equation with random initial data

1998 ◽  
Vol 64 (6) ◽  
pp. 704-713 ◽  
Author(s):  
Yu. Yu. Bakhtin
2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Joshua A. McGinnis ◽  
J. Douglas Wright

<p style='text-indent:20px;'>We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially varying material coefficients. Using the methods of stochastic homogenization we show that solutions with long wave initial data converge in an appropriate sense to solutions of a wave equation. The convergence is strong and both almost sure and in expectation, but the rate is quite slow. The technique combines energy estimates with powerful classical results about random walks, specifically the law of the iterated logarithm.</p>


1970 ◽  
Vol 41 (3) ◽  
pp. 945-955 ◽  
Author(s):  
R. P. Pakshirajan ◽  
M. Sreehari

1987 ◽  
Vol 74 (3) ◽  
pp. 319-340 ◽  
Author(s):  
J. Kuelbs ◽  
M. Ledoux

Author(s):  
Klaudiusz Czudek ◽  
Tomasz Szarek ◽  
Hanna Wojewódka-Ściążko

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