scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

A Method Of Solving A Non-Stationary Problem Of Ship Waves Excitation By A Submerged Object

2015 ◽  
Vol 10 (4) ◽  
pp. 43-59
Author(s):  
Andrey Arzhannikov ◽  
Igor Kotelnikov
Keyword(s):  
Exact Solution ◽  
Constant Velocity ◽  
Liquid Surface ◽  
Stationary Problem ◽  
Variable Velocity ◽  
Ship Waves ◽  
One Dimensional ◽  
Asymptotic Expressions ◽  
Dimensional Integral ◽  
Kelvin Wedge

We propose and develop a method of solving the problem of exciting ship waves by a submerged object that moves in a non-viscous fluid at a variable velocity. The case of the flush ball moving at constant velocity parallel to the surface of the liquid is considered to validate the proposed method by comparing the results with data reported earlier by other authors. Asymptotic expressions are derived describing the elevation of the liquid surface in the limit of small and large values of the Froude number. The exact solution is represented as two summands, each of them being reduced to one-dimensional integral. One summand describes the “Bernoulli hump”, and another - the “Kelvin wedge.”

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

An exact solution for one-dimensional unsteady nonlinear groundwater flow

Meccanica ◽  
1991 ◽  
Vol 26 (2-3) ◽  
pp. 129-133
Author(s):  
Vittorio di Federico
Keyword(s):  
Exact Solution ◽  
Groundwater Flow ◽  
One Dimensional

Exact solution for the charge soliton in a one-dimensional array of small tunnel junctions

1994 ◽  
Vol 49 (23) ◽  
pp. 16773-16776 ◽  
Author(s):  
G. Y. Hu ◽  
R. F. O’Connell
Keyword(s):  
Exact Solution ◽  
Tunnel Junctions ◽  
One Dimensional ◽  
Dimensional Array
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