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Page 8464 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
The Burgers equation u, + uu, = vux, + F,(t, x) is considered with a forcing term F(t, x) of period one in both variables ¢ and x.  ...  (CH-ETHZ; Ziirich) On the forced Burgers equation with periodic boundary conditions. Differential equations: La Pietra 1996 (Florence), 133-153, Proc. Sympos. Pure Math., 65, Amer. Math.  ... 

Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

N. Smaoui, B. Chentouf, A. Alalabi
2019 Advances in Difference Equations  
In this paper, we study the modelling and nonlinear boundary stabilization problem of the modified generalized Korteweg-de Vries-Burgers equation (MGKdVB) when the spatial domain is [0, 1].  ...  Then, two nonlinear boundary controllers are proposed for this equation and the L 2 -global exponential stability of the solution is shown.  ...  Acknowledgements The authors would like to thank the two anonymous referees for their feedbacks that truly improved the presentation of the final version of the manuscript.  ... 
doi:10.1186/s13662-019-2376-x fatcat:7ega53aiundvjkzkw6dyecwuie

Controllability Aspects of the Korteweg-de Vries Burgers Equation on Unbounded Domains [article]

F.A. Gallego
2017 arXiv   pre-print
The aim of this work is to consider the controllability problem of the linear system associated to Korteweg-de Vries Burgers equation posed in the whole real line.  ...  We obtain a sort of exact controllability for solutions in L^2_loc(^2) by deriving an internal observability inequality and a Global Carlemann estimate.  ...  The author would like to thank professor A. F. Pazoto (UFRJ) for the very useful suggestions given during the elaboration of this paper.  ... 
arXiv:1702.05631v1 fatcat:hk7stebh3vcnteuqdxoso7fxbi

Solving Partial Differential Equations Using Deep Learning and Physical Constraints

Yanan Guo, Xiaoqun Cao, Bainian Liu, Mei Gao
2020 Applied Sciences  
In this study, we use the method to study the wave equation, the KdV–Burgers equation, and the KdV equation.  ...  The various studies of partial differential equations (PDEs) are hot topics of mathematical research.  ...  Besides, Equation (15) becomes the Korteweg-de Vries (KdV) equation when β is zero. u t + αuu x + γu xxx = 0 (17) The Korteweg-de Vries (KdV) equation was first introduced in 1985 by Korteweg and de  ... 
doi:10.3390/app10175917 fatcat:wlhw63csmvabjb37fhpdrmi6qe

Distributed Control of the Generalized Korteweg-de Vries-Burgers Equation

Nejib Smaoui, Rasha H. Al-Jamal
2008 Mathematical Problems in Engineering  
The paper deals with the distributed control of the generalized Kortweg-de Vries-Burgers equation (GKdVB) subject to periodic boundary conditions via the Karhunen-Loève (K-L) Galerkin method.  ...  Finally, three state feedback linearization control schemes with the objective of enhancing the stability of the GKdVB equation are proposed.  ...  Mathematical Problems in Engineering For future work, we will look into the development of adaptive and optimal control schemes for the GKdVB equation, and the design of boundary controllers for different  ... 
doi:10.1155/2008/621672 fatcat:p4fq3xpnbzepdobvc4itwfxzgm

A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks [article]

Chenxi Wu, Min Zhu, Qinyang Tan, Yadhu Kartha, Lu Lu
2022 arXiv   pre-print
with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training.  ...  The distribution of these points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used.  ...  i = 1000 for the Korteweg-de Vries equation in Section 3.7.  ... 
arXiv:2207.10289v1 fatcat:z2nfwgf6z5dhrlt4xl7pta53we

Influence of parametric forcing on the nonequilibrium dynamics of wave patterns

S. I. Abarzhi, O. Desjardins, A. Nepomnyashchy, H. Pitsch
2007 Physical Review E  
We investigate analytically and numerically the effect of inhomogeneities on the nonequilibrium dynamics of wave patterns in the framework of a complex Ginzburg-Landau equation ͑CGLE͒ with parametric,  ...  We consider the influence of modulations on the development of an intermittent chaos and show that the parametric forcing may completely suppress the appearance of chaotic patterns.  ...  Without forcing, for long-wave dynamics the evolution of phase disturbances in CGLE is governed in general by one of the following nonlinear equations: Burgers equation ͑i͒, dissipationmodified Korteweg-de  ... 
doi:10.1103/physreve.75.046208 pmid:17500979 fatcat:4tstf76wyjeaneill5yqivixrq

Deciding the Nature of the "Coarse Equation" through Microscopic Simulations: the Baby-Bathwater Scheme [article]

Ju Li, Panayotis G. Kevrekidis, C. William Gear, Ioannis G. Kevrekidis
2002 arXiv   pre-print
The closure is obtained "on demand" through appropriately initialized bursts of microscopic simulation.  ...  These decisions affect the number and type of boundary conditions as well as the nature of the algorithms employed in good solution practice.  ...  We will illustrate what we call the Baby-Bathwater algorithm on examples of particle systems realizing the Burgers and Korteweg-de Vries (KdV) equations, for the task of inferring the highest order of  ... 
arXiv:physics/0212034v1 fatcat:yf6awgiqwff75efn4pu4nzkaem

Deciding the Nature of the Coarse Equation through Microscopic Simulations: The Baby-Bathwater Scheme

Ju Li, Panayotis G. Kevrekidis, C. William Gear, Ioannis G. Kevrekidis
2003 Multiscale Modeling & simulation  
The closure is obtained "on demand" through appropriately initialized bursts of microscopic simulation.  ...  These decisions affect the number and type of boundary conditions as well as the nature of the algorithms employed in good solution practice.  ...  We will illustrate what we call the Baby-Bathwater algorithm on examples of particle systems realizing the Burgers and Korteweg-de Vries (KdV) equations, for the task of inferring the highest order of  ... 
doi:10.1137/s1540345902419161 fatcat:fpfbgi6cqzezrcotkuvoe3oi3m

Deciding the Nature of the Coarse Equation through Microscopic Simulations: The Baby-Bathwater Scheme

Ju Li, Panayotis G. Kevrekidis, C. William Gear, Ioannis G. Kevrekidis
2007 SIAM Review  
The closure is obtained "on demand" through appropriately initialized bursts of microscopic simulation.  ...  These decisions affect the number and type of boundary conditions as well as the nature of the algorithms employed in good solution practice.  ...  We will illustrate what we call the Baby-Bathwater algorithm on examples of particle systems realizing the Burgers and Korteweg-de Vries (KdV) equations, for the task of inferring the highest order of  ... 
doi:10.1137/070692303 fatcat:dbg4aoac5bhm3fh4a67urf4key

MPI-AMRVAC: a parallel, grid-adaptive PDE toolkit [article]

Rony Keppens, Jannis Teunissen, Chun Xia, Oliver Porth
2020 arXiv   pre-print
Korteweg-de Vries solutions generalizing early findings on soliton behaviour, shallow water applications in round or square pools, hydrodynamic convergence tests as well as challenging computational fluid  ...  We report on the latest additions to our open-source, block-grid adaptive framework MPI-AMRVAC, which is a general toolkit for especially hyperbolic/parabolic partial differential equations (PDEs).  ...  This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and  ... 
arXiv:2004.03275v1 fatcat:uvgqsxzwqvg37p4ivfyg5wxckm

MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit

Rony Keppens, Jannis Teunissen, Chun Xia, Oliver Porth
2020 Computers and Mathematics with Applications  
Korteweg-de Vries solutions generalizing early findings on soliton behavior, shallow water applications in round or square pools, hydrodynamic convergence tests as well as challenging computational fluid  ...  We report on the latest additions to our open-source, block-grid adaptive framework MPI-AMRVAC, which is a general toolkit for especially hyperbolic/parabolic partial differential equations (PDEs).  ...  The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation Flanders (FWO) and the Flemish Government -department  ... 
doi:10.1016/j.camwa.2020.03.023 fatcat:dzuik6zqeng2tn5jd6k4amtxc4

Wind-Induced Changes to Shoaling Surface Gravity Wave Shape [article]

Thomas Zdyrski, Falk Feddersen
2022 arXiv   pre-print
We derive a variable-coefficient Korteweg-de Vries-Burgers (vKdV-B) equation governing the wave profile's evolution and solve it numerically using a Runge-Kutta third-order finite difference solver.  ...  However, the combined effect of shoaling and wind-forcing on wave shape, particularly relevant in the near shore environment, has not yet been investigated theoretically.  ...  We thank the National Science Foundation (OCE-1558695) and the Mark Walk Wolfinger Surfzone Processes Research Fund for their support of this work.  ... 
arXiv:2110.05519v2 fatcat:2yesle6l5fd2vlnhrfb5slz36q

Cauchy Processes, Dissipative Benjamin–Ono Dynamics and Fat-Tail Decaying Solitons

Max-Olivier Hongler
2021 Fractal and Fractional  
In this paper, a dissipative version of the Benjamin–Ono dynamics is shown to faithfully model the collective evolution of swarms of scalar Cauchy stochastic agents obeying a follow-the-leaderinteraction  ...  This behaviour can be clearly understood from the interaction of mutual agents.  ...  Solitary wave solutions of the compound Burgers-Korteweg-de Vries equation. Phys. A Stat. Mech. Appl. 2005, 352, 419–435. [CrossRef] 7. Feng, Z.S.; Meng, Q.G.  ... 
doi:10.3390/fractalfract6010015 fatcat:usuxhi3o2bgjjhrtfo6hiyvddy

Computing the weak limit of KdV

David W. McLaughlin, John A. Strain
1994 Communications on Pure and Applied Mathematics  
To contrast these different regularizations, we have used a numerical method described in Section 3.9 to solve both the Burgers and KdV equations at moderately small values of E.  ...  Figure 1 compares the short wavelength, finite amplitude oscillations of the KdV case to the smooth profile of the Burgers solution.  ...  The first author was funded in part by the Air Force Office of Scientific Research, AFOSR-90-0 16 1, and the National Science Foundation, DMS 8922717 A01.  ... 
doi:10.1002/cpa.3160471003 fatcat:fpe2fy37xvcarlksjvuifti4yy
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