A priori estimation of solutions of a boundary problem for a pseudodifferential equation with degeneration

2021 ◽  
pp. 6-10
Author(s):  
Alexander Dmitrievich Baev ◽  
◽  
Dmitry Alexandrovich Chechin ◽  
Sergey Alexandrovich Shabrov ◽  
Natalya Ivanovna Rabotinskaya ◽  
...  
Keyword(s):  
Boundary Problem ◽  
A Priori ◽  
Pseudodifferential Equation ◽  
A Priori Estimation

A Priori Estimation of Solutions of a Boundary Problem for a Pseudodifferential Equation with Degeneration

2021 ◽  
Vol 65 (5) ◽  
pp. 1-3
Author(s):  
A. D. Baev ◽  
D. A. Chechin ◽  
S. A. Shabrov ◽  
N. I. Rabotinskaya ◽  
N. A. Babaitseva
Keyword(s):  
Boundary Problem ◽  
A Priori ◽  
Pseudodifferential Equation ◽  
A Priori Estimation

Maximum a priori estimation of wavefront slopes using a Hartmann wavefront sensor

1996 ◽  
Author(s):  
Scott A. Sallberg ◽  
Byron M. Welsh ◽  
Michael C. Roggemann
Keyword(s):  
A Priori ◽  
Wavefront Sensor ◽  
A Priori Estimation

Genomic selection efficiency and a priori estimation of accuracy in a structured dent maize panel

2018 ◽  
Vol 132 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Simon Rio ◽  
Tristan Mary-Huard ◽  
Laurence Moreau ◽  
Alain Charcosset
Keyword(s):  
Genomic Selection ◽  
A Priori ◽  
Selection Efficiency ◽  
A Priori Estimation

scholarly journals A priori estimation of sequencing effort in complex microbial metatranscriptomes

2020 ◽  
Vol 10 (23) ◽  
pp. 13382-13394 ◽  
Author(s):  
Toni Monleon‐Getino ◽  
Jorge Frias‐Lopez
Keyword(s):  
A Priori ◽  
A Priori Estimation

scholarly journals Bifurcation Behaviors of Steady-State Solution to a Discrete General Brusselator Model

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ruyun Ma ◽  
Zhongzi Zhao
Keyword(s):  
A Priori ◽  
Global Bifurcation ◽  
Small Neighborhood ◽  
Steady State Solution ◽  
Solution Curve ◽  
Bifurcation Theorem ◽  
Brusselator Model ◽  
Constant Solution ◽  
A Priori Estimation ◽  
Increasing Function

We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model. We generalize the linear u in the standard Brusselator model to the nonlinear fu. Assume that f∈C0,∞,0,∞ is a strictly increasing function, and f′f−1a∈0,∞. Taking b as the bifurcation parameter, we obtain that the solution set of the problem constitutes a constant solution curve and a nonconstant solution curve in a small neighborhood of the bifurcation point b0j,f−1a,ab/f−1a2. Moreover, via the Rabinowitz bifurcation theorem, we obtain the global structure of the set of nonconstant solutions under the condition that fs/s2 is nonincreasing in 0,∞. In this process, we also make a priori estimation for the nonnegative nonconstant solutions of the problem.

scholarly journals A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170385 ◽  
Author(s):  
Ayoub Gouasmi ◽  
Eric J. Parish ◽  
Karthik Duraisamy
Keyword(s):  
Evolution Equations ◽  
Nonlinear Dynamical Systems ◽  
A Priori ◽  
Time History ◽  
Original System ◽  
Memory Kernel ◽  
Nonlinear Dynamical ◽  
History Of ◽  
Consistent Basis ◽  
A Priori Estimation

Reduced models of nonlinear dynamical systems require closure, or the modelling of the unresolved modes. The Mori–Zwanzig procedure can be used to derive formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the time history of the resolved variables. While this procedure does not reduce the complexity of the original system, these equations can serve as a mathematically consistent basis to develop closures based on memory approximations. In this scenario, knowledge of the memory kernel is paramount in assessing the validity of a memory approximation. Unravelling the memory kernel requires solving the orthogonal dynamics, which is a high-dimensional partial differential equation that is intractable, in general. A method to estimate the memory kernel a priori , using full-order solution snapshots, is proposed. The key idea is to solve a pseudo orthogonal dynamics equation, which has a convenient Liouville form, instead. This ersatz arises from the assumption that the semi-group of the orthogonal dynamics is a composition operator for one observable. The method is exact for linear systems. Numerical results on the Burgers and Kuramoto–Sivashinsky equations demonstrate that the proposed technique can provide valuable information about the memory kernel.

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