The global existence and attractor for p-Laplace equations in unbounded domains

Autor:	Chenyin Qian, Reinhard Farwig
Rok vydání:	2020
Předmět:	Numerical Analysis Nonlinear system Pure mathematics Partial differential equation Compact space Laplace transform Semigroup Applied Mathematics Bounded function Attractor Analysis Domain (mathematical analysis) Mathematics
Zdroj:	Journal of Elliptic and Parabolic Equations. 6:311-342
ISSN:	2296-9039 2296-9020
DOI:	10.1007/s41808-020-00067-9
Popis:	The asymptotic behavior for a class of parabolic p-Laplace equations in an open bounded or unbounded domain of $${\mathbb{R}}^N$$ R N is investigated. Based on a general condition on the nonlinearity f(x, u) and the invading domain technique, the global well-posedness of the equation is established. By proving the $$\omega$$ ω -limit compactness of the continuous semigroup, the existence of the global attractor for the equation is obtained. Besides, in case of bounded domains, we also get estimates of the finite fractal dimension of the global attractor based on the classical method of $$\ell$$ ℓ -trajectories.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::21fbb04e5ec6fffd1ee0a2541ddf1829 https://doi.org/10.1007/s41808-020-00067-9 Zobrazit plný text záznamu Full text from SpringerLink