An initial-boundary value problem for the one-dimensional rotating shallow water magnetohydrodynamic equations

Ye, Jane J.; Guo, Hongjun; Hu, Yanbo

doi:10.1016/j.jmaa.2023.127422

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…It is worth remembering that the (joint) objective of the present work together with [1], which replicates the scheme of [8] for a more general thermoelasticity model, is the investigation of the well-posedness issue of the model itself, combined with the study of the spatial behavior of the solution, in the sense that the identification of explicit solutions for the above-proposed models (i.e., initial-boundary value problems) is not among the goals of such studies. In a near future, it would be interesting to make advances in this sense, as for example in [10], where a general solution is presented for the Lord-Shulman thermoelasticity model in transversely isotropic solids, proving its completeness (such general solution is also detailed for various combinations of (thermo)elastodynamic and elastostatic theories for transversely isotropic and isotropic media) or even in [11], and, very recently, in [12], or [13], in which numerical techniques are also employed.…”

Section: Introductionmentioning

confidence: 99%

Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times

Carini,

Zampoli

2023

Mathematics

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This brief contribution aims to complement a study of well-posedness started by the same authors in 2020, showing—for that same mathematical model—the existence of a domain of influence of external data. The object of investigation, we recall, is a linear thermoelastic model with a porous matrix modeled on the basis of the Cowin–Nunziato theory, and for which the heat exchange phenomena are intended to obey a time-differential heat transfer law with three delay times. We therefore consider, without reporting it explicitly, the (suitably adapted) initial-boundary value problem formulated at that time, as well as some analytical techniques employed to handle it in order to address the uniqueness and continuous dependence questions. Here, a domain of influence theorem is proven, showing the spatial behavior of the solution in a cylindrical domain, by activating the hypotheses that make the model thermodynamically consistent. The theorem, in detail, demonstrates that for a finite time t>0, the assigned external (thermomechanical) actions generate no disturbance outside a bounded domain contained within the cylindrical region of interest. The length of the work is deliberately kept to a minimum, having opted where possible for bibliographic citations in favor of greater reading fluency.

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Section: Introductionmentioning

confidence: 99%

Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times

Carini,

Zampoli

2023

Mathematics

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Lie symmetries for the shallow water magnetohydrodynamics equations in a rotating reference frame

Paliathanasis,

Halder

2024

Phys. Scr.

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We perform a detailed Lie symmetry analysis for the hyperbolic system of partial diﬀerential equations that describe the one-dimensional Shallow Water magnetohydrodynamics equations within a rotating reference frame. We consider a relaxing condition ∇(hB)!= 0 for the one-dimensional problem, which has been used to overcome unphysical behaviors. The hyperbolic system of partial diﬀerential equations depends on two parameters: the constant gravitational potential g and the Coriolis term f0, related to the constant rotation of the reference frame. For four diﬀerent cases, namely g = 0, f0 = 0; g ?= 0 , f0 = 0; g = 0, f0 ?= 0; and g ?= 0, f0 ?= 0 the admitted Lie symmetries for the hyperbolic system form diﬀerent Lie algebras. Speciﬁcally the admitted Lie algebras are the G10 = {A3,3 ⊗s A2,1} ⊗s A5a,34; G8 = A2,1 ⊗s A6,22; G7 = A3,5 ⊗s {A2,1 ⊗s A2,1}; and G6 = A3,5 ⊗s A3,3 respectively, where we use the Morozov-Mubarakzyanov-Patera

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An initial-boundary value problem for the one-dimensional rotating shallow water magnetohydrodynamic equations

Cited by 2 publications

References 34 publications

Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times

Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times

Lie symmetries for the shallow water magnetohydrodynamics equations in a rotating reference frame

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