Details
| Original language | English |
|---|---|
| Pages (from-to) | 459-480 |
| Number of pages | 22 |
| Journal | Journal of Evolution Equations |
| Volume | 12 |
| Issue number | 2 |
| Publication status | Published - 20 Mar 2012 |
Abstract
The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in a given (two-scale) domain in Euclidean space. The main objective is to establish the local well-posedness in the strong sense of the flow. Two main settings are investigated: semilinear systems with linear boundary conditions and semilinear systems with nonlinear boundary conditions. With the help of analytic semigroups, we establish local well-posedness and investigate the long-time behavior of the solutions in the first case: we establish global existence and show that solutions converge to zero at an exponential rate.
Keywords
- Compressible newtonian fluid, Double porosity, Parabolic evolution equation, Porous medium, Two-scale model
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Journal of Evolution Equations, Vol. 12, No. 2, 20.03.2012, p. 459-480.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Strong solutions of semilinear matched microstructure models
AU - Escher, Joachim
AU - Treutler, Daniela
N1 - Funding information: Mathematics Subject Classification: AMS 35K58, 35B40, 76N10 Keywords: Porous medium, Double porosity, Two-scale model, Parabolic evolution equation, Compressible newtonian fluid. This work was completed with the support of the German research foundation (DFG).
PY - 2012/3/20
Y1 - 2012/3/20
N2 - The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in a given (two-scale) domain in Euclidean space. The main objective is to establish the local well-posedness in the strong sense of the flow. Two main settings are investigated: semilinear systems with linear boundary conditions and semilinear systems with nonlinear boundary conditions. With the help of analytic semigroups, we establish local well-posedness and investigate the long-time behavior of the solutions in the first case: we establish global existence and show that solutions converge to zero at an exponential rate.
AB - The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in a given (two-scale) domain in Euclidean space. The main objective is to establish the local well-posedness in the strong sense of the flow. Two main settings are investigated: semilinear systems with linear boundary conditions and semilinear systems with nonlinear boundary conditions. With the help of analytic semigroups, we establish local well-posedness and investigate the long-time behavior of the solutions in the first case: we establish global existence and show that solutions converge to zero at an exponential rate.
KW - Compressible newtonian fluid
KW - Double porosity
KW - Parabolic evolution equation
KW - Porous medium
KW - Two-scale model
UR - http://www.scopus.com/inward/record.url?scp=84861454992&partnerID=8YFLogxK
U2 - 10.1007/s00028-012-0140-8
DO - 10.1007/s00028-012-0140-8
M3 - Article
AN - SCOPUS:84861454992
VL - 12
SP - 459
EP - 480
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
IS - 2
ER -