Details
| Original language | English |
|---|---|
| Pages (from-to) | 463-510 |
| Number of pages | 48 |
| Journal | Nonlinear Differential Equations and Applications NoDEA |
| Volume | 2 |
| Issue number | 4 |
| Publication status | Published - Dec 1995 |
| Externally published | Yes |
Abstract
This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law. We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Nonlinear Differential Equations and Applications NoDEA, Vol. 2, No. 4, 12.1995, p. 463-510.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Maximal regularity for a free boundary problem
AU - Escher, Joachim
AU - Simonett, Gieri
PY - 1995/12
Y1 - 1995/12
N2 - This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law. We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.
AB - This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darcy's law. We prove existence of a unique maximal classical solution, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.
UR - http://www.scopus.com/inward/record.url?scp=0000433754&partnerID=8YFLogxK
U2 - 10.1007/BF01210620
DO - 10.1007/BF01210620
M3 - Article
AN - SCOPUS:0000433754
VL - 2
SP - 463
EP - 510
JO - Nonlinear Differential Equations and Applications NoDEA
JF - Nonlinear Differential Equations and Applications NoDEA
SN - 1021-9722
IS - 4
ER -