Application of accretive operators theory to evolutive combined conduction, convection and radiation

“…which is easily derived from Equation (7). When l A and l B are functions of time t, one can apply the previous results at every time t and obtain…”

Section: The Second Order Ode Reformulationmentioning

confidence: 99%

“…Equation ( 1) is a heat equation, with a heat sourcef , where conduction and convection have been neglected, but that brings the effect of the radiation into play, which obliges to include Equation (2). 1 For situations where the S 2 approximation is not accurate enough, more complete mathematical models can be consulted in references [5,7,8].…”

Section: Introductionmentioning

confidence: 99%

About the solution of the even parity formulation of the transient radiative heat transfer equations

López-Pouso

Muñoz-Sola

2010

Rev. R. Acad. Cien. Serie A. Mat.

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This paper studies the existence and uniqueness questions, in classical spaces, for a certain system of differential equations. From the physical point of view, the interest of this system lies in that it becomes, for particular choices of its coefficients, the even parity formulation of the S2 approximation of the transient radiative heat transfer equations in the one-dimensional slab. A priori lower and upper bounds of the solution are obtained as well.Sobre la solución de la formulación par de las ecuaciones evolutivas de transferencia de calor por radiaciónResumen. Este artículo aborda las cuestiones de existencia y unicidad, en espacios clásicos, para cierto sistema de ecuaciones diferenciales. Desde el punto de vista físico, el interés de este sistema radica en que se convierte, para elecciones particulares de sus coeficientes, en la formulación par de la aproximación S2 de las ecuaciones evolutivas de la tranferencia de calor por radiación en una geometría de laja (slab) unidimensional. Asimismo, se obtienen cotas a priori, tanto inferiores como superiores, de la solución.

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“…A lot of literature is devoted to the mathematical analysis and numerical computations of the radiative heat transfer system [32,3,25,39,9,23]. Besides the work [31] on the same model considered here, there are some works on similar models [40,28,2,1,26]. For example, the existence and uniqueness of strong solutions for the non-grey coupled convection-conduction radiation system were proved in [40] using accretive operators theory.…”

Section: Introductionmentioning

confidence: 99%

On the diffusive limits of radiative heat transfer system I: well prepared initial and boundary conditions

Gabsi¹,

Huo²,

Masmoudi³

2020

Preprint

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We study the diffusive limit approximation for a radiative heat transfer system under three different types of boundary conditions. We prove the global existence of weak solutions for this system by using a Galerkin method. Using the compactness method, averaging lemma and Young measure theory, we prove that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial and boundary layer exist. Contents 42 Appendix A. Lemmas used in the Compactness Method 44 Appendix B. Basis in L 2 (Ω × S 2 ) 46

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Application of accretive operators theory to evolutive combined conduction, convection and radiation

Cited by 16 publications

References 7 publications

Existence and bounds for the half-moment entropy approximation to radiative transfer

Existence and bounds for the half-moment entropy approximation to radiative transfer

About the solution of the even parity formulation of the transient radiative heat transfer equations

On the diffusive limits of radiative heat transfer system I: well prepared initial and boundary conditions

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