𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Stability of Markov Semigroups and Applications to Parabolic Systems

✍ Scribed by Katarzyna Pichór; Ryszard Rudnicki


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
264 KB
Volume
215
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis


A new theorem for asymptotic stability of Markov semigroups is proved. This result is applied to semigroups generated by parabolic systems describing the evolution of densities of two-state diffusion processes. ᮊ 1997 Academic Press Ž . Ѩt Ž .


📜 SIMILAR VOLUMES


Decay of Heat Semigroups in L∞ and Appli
✍ Philippe Souplet 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 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 Ä . 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

Existence and stability of steady soluti
✍ Hua Chen; Xin-Hua Zhong 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 118 KB

## Abstract In this paper, we study the existence of non‐constant steady solutions and the linear stability of constant solutions to nonlinear parabolic‐elliptic system, which actually is a simplified form of the Keller–Segel system modelling chemotaxis. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, We

Asymptotic analysis of solutions to para
✍ Vladimir Kozlov; Mikael Langer; Peter Rand 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 274 KB

## Abstract We study asymptotics as __t__ → ∞ of solutions to a linear, parabolic system of equations with time‐dependent coefficients in Ω × (0, ∞), where Ω is a bounded domain. On __∂__ Ω × (0, ∞) we prescribe the homogeneous Dirichlet boundary condition. For large values of __t__, the coefficien