Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary p-summable right-hand side

Druet, Pierre-Etienne

doi:10.1007/s10492-010-0005-9

Cited by 18 publications

(11 citation statements)

References 14 publications

(25 reference statements)

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“…Transmission problems in separated and disconnected domains are represented by systems of partial differential equations [26] with additional conditions (initial and boundary conditions, nonlocal jump conditions). The problems of such types were investigated by many authors [5,6,8,16,24]. In particular, an one and two-dimensional elliptic problem in two disjoint domains was studied in [14,17,22].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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Parabolic-hyperbolic transmission problem in disjoint domains

Milovanovic-Jeknic¹

2018

Filomat

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In applications, especially in engineering, often are encountered composite or layered structures, where the properties of individual layers can vary considerably from the properties of the surrounding material. Layers can be structural, thermal, electromagnetic or optical, etc. Mathematical models of energy and mass transfer in domains with layers lead to so called transmission problems. In this paper we investigate a mixed parabolic-hyperbolic initial-boundary value problem in two nonadjacent rectangles with nonlocal integral conjugation conditions. It was considered more examples of physical and engineering tasks which are reduced to transmission problems of similar type. For the model problem the existence and uniqueness of its weak solution in appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed.

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Section: Formulation Of the Problemmentioning

confidence: 99%

“…Let u = (u 1 , u 2 ) be the solution of the problem (1)- (8) and v = (v 1 , v 2 ) the solution of finite difference scheme (16)- (26). Then the error z = u − v satisfies the following finite difference scheme:…”

Section: Convergence Of the Finite Difference Schemementioning

confidence: 99%

Parabolic-hyperbolic transmission problem in disjoint domains

Milovanovic-Jeknic¹

2018

Filomat

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“…In the past 30 years, a large number of papers have been devoted to the solvability of complex heat transfer problems in radiation‐opaque or radiation‐semitransparent materials (cf. other works 16–47,48–64 ). Note that, in the literature, 46–51,53,59–64 the radiation transfer equation is changed by its diffusion P 1 approximation.…”

Section: Introductionmentioning

confidence: 96%

Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies

Амосов

2021

Math Methods in App Sciences

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We consider a stationary boundary value problem describing a radiative‐conductive heat transfer in a system consisting of one absolutely black body and several semitransparent bodies. To describe the radiative transfer, the integro‐differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. We proved at the first time the unique solvability of this problem. Besides, we proved the comparison theorems and established the results on improving the properties of solutions with increasing exponents of data summability.

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“…[3,4,22,28,30] and the references therein). Here, we adopt this approach to determine explicit estimates for the Cauchy problem inspired in the nonlinear heat equation with the Neumann condition on one part of the boundary of the domain, and the power law condition on the remaining part of the boundary that includes the radiative effects [9,13]. Also the constants involved in L p,∞ -estimate are determined.…”

Section: Introductionmentioning

confidence: 99%