On a System of Equations of Evolution with a Non-Symmetrical Parabolic Part Occuring in the Analysis of Moisture and Heat Transfer in Porous Media

Vála, Jiří

doi:10.1023/a:1021741320045

Cited by 13 publications

(12 citation statements)

References 17 publications

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“…The strong solution [θ ε , w ε ] ∈ V 2,1 2 (Q T ) of the problem (34)-(43) (ensured by Theorem 4) is a solution of the system (31)- (33) with the boundary and initial conditions (37)-(43) and satisfies the variational problem (corresponding to (31)-(33) and (37)-(43))…”

Section: Passage To the Limit For ε →mentioning

confidence: 99%

Global weak solutions for coupled transport processes in concrete walls at high temperatures

Beneš

Štefan

2012

Z Angew Math Mech

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Key wordsInitial-boundary value problems for second-order parabolic systems, nonlinear boundary conditions, global existence of weak solutions, coupled heat and mass transport.We consider an initial-boundary value problem for a fully nonlinear coupled parabolic system with nonlinear boundary conditions modeling hygro-thermal behavior of concrete at high temperatures. We prove a global existence of a weak solution to this system on any physically relevant time interval. The main result is proved by an approximation procedure. This consists in proving the existence of solutions to mollified problems using the Leray-Schauder theorem, for which a priori estimates are obtained. The limit then provides a weak solution for the original problem. A practical example illustrates a performance of the model for a problem of a concrete segment exposed to transient heating according to three different fire scenarios. Here, the focus is on the short-term pore pressure build up, which can lead to explosive spalling of concrete and catastrophic failures of concrete structures.

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Section: Passage To the Limit For ε →mentioning

confidence: 99%

Global weak solutions for coupled transport processes in concrete walls at high temperatures

Beneš

Štefan

2012

Z Angew Math Mech

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“…It can be studied without any knowledge of limit behaviour of microstructural terms: in more simple cases, especially for linear problems with p = 2,e. [15]. Let us also remark that in some seemingly simple problems, e. g. for the general formulation of transfer of heat and moisture (in various phases) through a porous medium, discussed in [19] with u = (r,0), containing some moisture potential O, with missing ko and k{u, VM) = K{u)'Vu for certain non-symmetric matrix K (even without any proper computational fluid dynamics), the existence of solution in the expectable weak (or variational) sense may be guaranteed only in very special cases (as in the classical Luikov theory) -cf.…”

Section: Existence and Convergence Questions Possible Generalizationsmentioning

confidence: 99%

On Two‐Scale Modelling of Heat and Mass Transfer

Vála¹,

Šťastník²

2008

AIP Conference Proceedings

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Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro-and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.

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“…However, these results are not applicable if B does not take the subgradient structure, which is the case of coupled balance equations for energy and mass transport. To the best of our knowledge, the only related works in this context are due to Vala [25], Li and Sun [18], Li et al [19] and Li and Sun [20]. Although the approach in [25] admits non-symmetry in the parabolic term, it requires unrealistic symmetry in the elliptic part.…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, the only related works in this context are due to Vala [25], Li and Sun [18], Li et al [19] and Li and Sun [20]. Although the approach in [25] admits non-symmetry in the parabolic term, it requires unrealistic symmetry in the elliptic part. The last-mentioned works, studying a model of specific structure of a heat and mass transfer arising from textile industry, prove the global existence for one-dimensional problems in [18,19] and three-dimensional problems in [20].…”

Section: Introductionmentioning

confidence: 99%

On doubly nonlinear elliptic-parabolic systems arising in coupled transport phenomena in unsaturated porous media

Beneš

Krupička

2014

Nonlinear Differ. Equ. Appl.

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We consider an initial-boundary value problem for a fully nonlinear degenerate parabolic system. The mathematical problem is originally motivated by coupled Richards and heat equations modelling hygrothermal flows in unsaturated porous media and fractured rock masses. We prove a global existence of a weak solution to this problem on an arbitrary interval of time. Mathematics Subject Classification (2010). Primary 35A01; Secondary 35K61, 80A20. Keywords. Initial-boundary value problems for second-order parabolic systems, Global existence of weak solutions, Coupled heat and mass transport in porous media. 122M. Beneš and L. Krupička NoDEA (A4) For initial data we assume u 0 , θ 0 ∈ L 2 (Ω).Vol. 22 (2015) On doubly nonlinear elliptic-parabolic systems 125

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On a System of Equations of Evolution with a Non-Symmetrical Parabolic Part Occuring in the Analysis of Moisture and Heat Transfer in Porous Media

Cited by 13 publications

References 17 publications

Global weak solutions for coupled transport processes in concrete walls at high temperatures

Global weak solutions for coupled transport processes in concrete walls at high temperatures

On Two‐Scale Modelling of Heat and Mass Transfer

On doubly nonlinear elliptic-parabolic systems arising in coupled transport phenomena in unsaturated porous media

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