Free boundary problems: the forefront of current and future developments

Shahgholian, Henrik; Vazquez, J. L.

doi:10.1098/rsta.2014.0285

Cited by 23 publications

(23 citation statements)

References 32 publications

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“…Permafrost phenomena or dynamics of snow avalanches are examples of natural situations whose study involves phase-change processes, some recent articles in these subjects are [1,6,20]. We refer the reader to [10,32] and the references therein for a recent survey in applications and future challenges in free boundary problems. Other references can be seen in the last published Free Boundary Problems International Conference Proceedings [16].…”

Section: Introductionmentioning

confidence: 99%

An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition

Ceretani

Salva

Tarzia

2018

Nonlinear Analysis: Real World Applications

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In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a generalized modified error function which is defined as the solution to a nonlinear ordinary differential problem of second order. It is proved that the latter has a unique non-negative bounded analytic solution when the parameter on which it depends assumes small positive values. Moreover, it is shown that the generalized modified error function is concave and increasing, and explicit approximations are proposed for it. Relation between the Stefan problem considered in this article with those with either constant thermal conductivity or a temperature boundary condition is also analysed.

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Section: Introductionmentioning

confidence: 99%

An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition

Ceretani

Salva

Tarzia

2018

Nonlinear Analysis: Real World Applications

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“…Free and moving boundary problems [1,2], where the problem domain is a priori unknown are encountered in different areas of science and engineering [3], including laser drilling of metals [4,5], crack propagation and delamination in composite materials [6,7], in Hele-Shaw flow [8,9], and elastic and plastic torsion [10,11].…”

Section: Introductionmentioning

confidence: 99%

A scalar prototype problem of deep abrasive drilling with an infinite free boundary: an asymptotic modeling study

Argatov

2019

J Eng Math

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A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a priori unknown domain with overdetermined boundary conditions, the right-hand sides of which depend on the unit normal to the free boundary. A perturbation analysis of the nonstandard free boundary problem that models deep abrasive drilling has been performed under the assumption that the free boundary is close to the surface of a given semi-infinite cylinder, the longitudinal position of which depends on the boundary data, and the leading-order asymptotic solution has been developed.

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“…The theory of free boundaries has seen great progress in the last half century. For the general literature up to 2015, we refer to [4,5]. Present study is devoted to theoretical investigation and mathematical modeling of arc phenomena in electrical contacts and appears as a continuation of recent studies where mathematical modeling of short arcing is considered [6,7].…”

Section: Introductionmentioning

confidence: 99%

Solution of an Inverse Two Phase Spherical Stefan Test Problem

Sarsengeldin

Nauryz

Bizhigitova

et al. 2017

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper, we represent the exact solution of a two phase inverse spherical Stefan problem, where along with unknown temperature functions heat flux function has to be determined. Suggested solution is obtained from new form of integral error function and its properties which are represented in the form of series whose coefficients have to be determined. The model problem can be used for mathematical modeling and investigation of arc phenomena in electrical contacts.MSC: 80A22; 33B20

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Free boundary problems: the forefront of current and future developments

Cited by 23 publications

References 32 publications

An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition

An exact solution to a Stefan problem with variable thermal conductivity and a Robin boundary condition

A scalar prototype problem of deep abrasive drilling with an infinite free boundary: an asymptotic modeling study

Solution of an Inverse Two Phase Spherical Stefan Test Problem

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