Higher-Order for the Multidimensional Generalized BBM-Burgers Equation: Existence and Convergence Results

Kondo, Cezar I.; Webler, Claudete M.

doi:10.1007/s10440-009-9531-4

Cited by 7 publications

(2 citation statements)

References 11 publications

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“…In the aspect of mathematical theory, Zhao et al consider the existence of the generalized BBM-Burgers equation with a dissipative term and verify the corresponding convergence in H-measures [13,14]. Kondo and Webler apply kinetic decomposition for the generalized BBM-Burgers equations with a dissipative term to obtain the approximate transport equation, and then take advantage of the averaging lemma to get the convergence [15]. Seok states the existence and conservation laws of the generalized BBM-Burgers equation with a dissipative term [16].…”

Section: Introductionmentioning

confidence: 99%

“…Seok states the existence and conservation laws of the generalized BBM-Burgers equation with a dissipative term [16]. For more theoretical analyses, refer to the references in [13][14][15][16]. In the aspect of numerical solutions, many methods have been used, like Painlev' e test, Darboux Transformation, bilinear method, symmetry method [17], and so on [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

Gao

et al. 2017

Discrete Dynamics in Nature and Society

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A finite element model is proposed for the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation with a high-order dissipative term; the scheme is based on adaptive moving meshes. The model can be applied to the equations with spatial-time mixed derivatives and high-order derivative terms. In this scheme, new variables are needed to make the equation become a coupled system, and then the linear finite element method is used to discretize the spatial derivative and the fifth-order Radau IIA method is used to discretize the time derivative. The simulations of 1D and 2D BBM-Burgers equations with high-order dissipative terms are presented in numerical examples. The numerical results show that the method keeps a second-order convergence in space and provides a smaller error than that based on the fixed mesh, which demonstrates the effectiveness and feasibility of the finite element method based on the moving mesh. We also study the effect of the dissipative terms with different coefficients in the equation; by numerical simulations, we find that the dissipative term plays a more important role than in dissipation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

Gao

et al. 2017

Discrete Dynamics in Nature and Society

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On the singular limit of a two‐phase flow equation with heterogeneities and dynamic capillary pressure

Kissling

Karlsen

2013

Z Angew Math Mech

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We consider conservation laws with spatially discontinuous flux that are perturbed by diffusion and dispersion terms. These equations arise in a theory of two‐phase flow in porous media that includes rate‐dependent (dynamic) capillary pressure and spatial heterogeneities. We investigate the singular limit as the diffusion and dispersion parameters tend to zero, showing strong convergence towards a weak solution of the limit conservation law.

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Large-time behavior for the solution to the generalized Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space

Wang

Zhang

2014

Journal of Mathematical Analysis and Applications

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Higher-Order for the Multidimensional Generalized BBM-Burgers Equation: Existence and Convergence Results

Abstract: We study the global existence of solutions for the multidimensional generalized BBM-Burgers equations of the form

Cited by 7 publications

References 11 publications

Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

On the singular limit of a two‐phase flow equation with heterogeneities and dynamic capillary pressure

Large-time behavior for the solution to the generalized Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space

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