About the Benjamin-Bona-Mahony Equation in Domains with Moving Boundary

Caldas, C. S. Q. De; Límaco, J.; Barreto, Rioco Kamei; Gamboa, Pedro

doi:10.5540/tema.2007.08.03.0329

“…Concerning mathematical free-boundary problems arising from singular interfaces, there are some results for a spatially onedimensional setting. We refer to [44,45] for application to solid mechanics and, for an application to moving reaction fronts in concrete, to [46][47][48]. Moreover, further challenges consist of developing suitable numerical algorithms and performing simulations in order to deal with applications.…”

Section: Functionality Of Interfacesmentioning

confidence: 99%

“…Such interfaces are dealt with in [4,11,27,28,34,58,59]. A special case of type S-I is mathematically dealt with in [44,45].…”

Section: Thermodynamically Non-active Interfaces [Type I]mentioning

confidence: 99%

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Continuous bodies with thermodynamically active singular sharp interfaces

Wolff

¹

,

Böhm

²

2016

Mathematics and Mechanics of Solids

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The subject of this comprehensive study is the general (mathematical) modeling of sharp (i.e. two-dimensional) interfaces without and with their own thermodynamical activity. We provide essential tools for the modeling of body-interface systems. Important items of the kinematics of singular (moving) interfaces as well as balance equations at interfaces will be addressed. Problems connected with material representation will be discussed. Special interfacial balances for mass, impulse, angular momentum, energy, mass of a tracer and of entropy will be considered including the discussion of special cases. As an illustrative example, a continuous model for a body with loss of material (e.g. due to mechanical treatment) will be developed in the framework presented.

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Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D

Zhang,

Li,

Su

2023

era

0

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<abstract><p>We study the Benjamin-Bona-Mahony model with finite distributed delay in 3D, which depicts the dispersive impact of long waves. Based on the well-posedness of model, the family of pullback attractors for the evolutionary processes generated by a global weak solution has been obtained, which is unique and minimal, via verifying asymptotic compactness in functional space with delay $ C_V $ and topological space $ V\times C_V $, where the energy equation method and a retarded Gronwall inequality are utilized.</p></abstract>

show abstract

Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D

Zhang,

Li,

Su

2023

era

0

View full text Add to dashboard Cite

<abstract><p>We study the Benjamin-Bona-Mahony model with finite distributed delay in 3D, which depicts the dispersive impact of long waves. Based on the well-posedness of model, the family of pullback attractors for the evolutionary processes generated by a global weak solution has been obtained, which is unique and minimal, via verifying asymptotic compactness in functional space with delay $ C_V $ and topological space $ V\times C_V $, where the energy equation method and a retarded Gronwall inequality are utilized.</p></abstract>

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About the Benjamin-Bona-Mahony Equation in Domains with Moving Boundary

Cited by 3 publications

References 8 publications

Continuous bodies with thermodynamically active singular sharp interfaces

Continuous bodies with thermodynamically active singular sharp interfaces

Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D

Dynamical behavior of Benjamin-Bona-Mahony system with finite distributed delay in 3D

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