𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Parabolic Systems in Unbounded Domains I. Existence and Dynamics

✍ Scribed by C.V Pao

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
303 KB
Volume
217
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we investigate the existence, uniqueness, and asymptotic behavior of a solution for a class of coupled nonlinear parabolic equations in a general unbounded domain that includes the whole space ‫ޒ‬ n , the exterior of a bounded domain, and a half space in ‫ޒ‬ n . The asymptotic behavior of the solution is with respect to a pair of quasi-solutions of the corresponding elliptic system, and when these two quasi-solutions coincide the solution of the parabolic system converges to a unique solution of the elliptic system.

πŸ“œ SIMILAR VOLUMES

Elliptic and parabolic problems in unbou
Elliptic and parabolic problems in unbounded domains
✍ Patrick Guidotti πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 181 KB

## Abstract We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative r

Decay of Heat Semigroups in L∞ and Appli
Decay of Heat Semigroups in L∞ and Applications to Nonlinear Parabolic Problems in Unbounded Domains
✍ Philippe Souplet πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 166 KB

We characterize all domains 0 of R N such that the heat semigroup decays in L(L (0)) or L(L 1 (0)) as t Γ„ . Namely, we prove that this property is equivalent to the Poincare inequality, and that it is also equivalent to the solvability of &2u= f in L (0) for all f # L (0). In particular, under mild

Infinite-dimensional exponential attract
Infinite-dimensional exponential attractors for fourth-order nonlinear parabolic equations in unbounded domains
✍ Messoud Efendiev πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 189 KB

## Communicated by W. Sprâßig We study in this article the long-time behavior of solutions of fourth-order parabolic equations in R 3 . In particular, we prove that under appropriate assumptions on the nonlinear interaction function and on the external forces, these equations possess infinite-dime

Attractors of reaction-diffusion systems
Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity
✍ Sergey V. Zelik πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 475 KB πŸ‘ 1 views

## Abstract The nonlinear reaction‐diffusion system in an unbounded domain is studied. It is proven that, under some natural assumptions on the nonlinear term and on the diffusion matrix, this system possesses a global attractor π’œ in the corresponding phase space. Since the dimension of the attract

Hausdorff dimension estimation for attra
Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: An example
✍ V. V. Chepyzhov; M. A. Efendiev πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 118 KB πŸ‘ 2 views

The subject of this paper is the asymptotic behavior of a class of nonautonomous, infinite-dimensional dynamical systems with an underlying unbounded domain. We present an approach that is able to overcome both the law of compactness of the trajectories and the continuity of the spectrum of the line