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Page 8464 of Mathematical Reviews Vol. , Issue 99m
[page]
1999
Mathematical Reviews
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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
2019
Advances in Difference Equations
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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]
2017
arXiv
pre-print
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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
2020
Applied Sciences
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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
2008
Mathematical Problems in Engineering
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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]
2022
arXiv
pre-print
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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
2007
Physical Review E
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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]
2002
arXiv
pre-print
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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
2003
Multiscale Modeling & simulation
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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
2007
SIAM Review
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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]
2020
arXiv
pre-print
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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
2020
Computers and Mathematics with Applications
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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]
2022
arXiv
pre-print
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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
2021
Fractal and Fractional
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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
1994
Communications on Pure and Applied Mathematics
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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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