排序方式: 共有13条查询结果,搜索用时 31 毫秒
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In this paper we analyze the abstract parabolic evolutionary equations
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Joachim Escher Gieri Simonett 《NoDEA : Nonlinear Differential Equations and Applications》1995,2(4):463-510
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.Supported by Schweizerischer Nationalfonds 相似文献
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We establish the equivalence between the family of uniformly regular Riemannian manifolds without boundary and the class of manifolds with bounded geometry. 相似文献
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Joachim?EscherEmail author Gieri?SimonettEmail author 《Journal of Evolution Equations》2003,3(4):549-576
It is shown that solutions to fully nonlinear parabolic evolution equations on symmetric
Riemannian manifolds are real analytic in space and time, provided the propagator is compatible
with the underlying Lie structure. Applications to Bellman equations and to a class of mean
curvature flows are also discussed. 相似文献
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We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a (unique)
solution that is analytic in space and time. 相似文献
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The volume preserving mean curvature flow near spheres 总被引:3,自引:0,他引:3
Joachim Escher Gieri Simonett 《Proceedings of the American Mathematical Society》1998,126(9):2789-2796
By means of a center manifold analysis we investigate the averaged mean curvature flow near spheres. In particular, we show that there exist global solutions to this flow starting from non-convex initial hypersurfaces.
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Jan Prüss Gieri Simonett Rico Zacher 《Archive for Rational Mechanics and Analysis》2013,207(2):611-667
We study the qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise herein, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria are studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening. 相似文献
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In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence,
uniqueness, and continuous dependence of solutions. Moreover, we give conditions for global existence and establish smoothness
properties of solutions. The results are based on maximal regularity estimates in continuous interpolation spaces. An important
new ingredient is that we are able to show that quasilinear parabolic evolution equations generate a smooth semiflow on the
trace spaces associated with maximal regularity, which are the natural phase spaces in this framework.
Received August 10, 2000; accepted September 20, 2000. 相似文献
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Gieri Simonett 《Journal of Mathematical Analysis and Applications》2006,324(1):580-603
We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting rates. Moreover, we prove global stability of the disease-free steady state. 相似文献