Incomplete Sobolev type equations of higher order with "white noise" in quasi-Banach spaces

2016 ◽  
Vol 10 ◽  
pp. 1811-1819
Author(s):  
Alyona A. Zamyshlyaeva ◽  
Evgeniy V. Bychkov ◽  
Olga N. Tsyplenkova
Keyword(s):  
White Noise ◽  
Banach Spaces ◽  
Higher Order ◽  
Sobolev Type

One Class of Sobolev Type Equations of Higher Order with Additive "White Noise"

2015 ◽  
Vol 15 (1) ◽  
pp. 185-196 ◽  
Author(s):  
Alyona A. Zamyshlyaeva ◽  
Georgy A. Sviridyuk ◽  
Angelo Favini
Keyword(s):  
White Noise ◽  
Higher Order ◽  
Sobolev Type ◽  
Additive White Noise

The phase spaces of a class of linear higher-order Sobolev type equations

2006 ◽  
Vol 42 (2) ◽  
pp. 269-278 ◽  
Author(s):  
G. A. Sviridyuk ◽  
A. A. Zamyshlyaeva
Keyword(s):  
Higher Order ◽  
Sobolev Type

scholarly journals Arbitrarily distortable Banach spaces of higher order

2016 ◽  
Vol 214 (2) ◽  
pp. 553-581 ◽  
Author(s):  
Kevin Beanland ◽  
Ryan Causey ◽  
Pavlos Motakis
Keyword(s):  
Banach Spaces ◽  
Higher Order

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

scholarly journals Higher order Gateaux smooth bump functions on Banach spaces

1995 ◽  
Vol 51 (2) ◽  
pp. 291-300 ◽  
Author(s):  
David P. McLaughlin ◽  
Jon D. Vanderwerff
Keyword(s):  
Banach Spaces ◽  
Higher Order ◽  
Smooth Approximation ◽  
Bump Function

For Г uncountable and p ≥ 1 odd, it is shown ℓp(г) admits no continuous p-times Gateaux differentiable bump function. A space is shown to admit a norm with Hölder derivative on its sphere if it admits a bounded bump function with uniformly directionally Hölder derivative. Some results on smooth approximation are obtained for spaces that admit bounded uniformly Gateaux differentiable bump functions.

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