CINECA IRIS Institutional Research Information System
IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili.
EnglishOf concern is the uniformly parabolic problem \begin{equation*} u_t =\dv(\A\nabla u),\qquad u(0,x)=f(x),\qquad u_t +\beta\pan u+\gamma u-q\beta \lb u=0, \end{equation*} for $x\in \Omega\subset \R^N$ and $t\ge0$. Here $\A=\{a_{ij}(x)\}_{ij}$ is a real, hermitian, uniformly positive definite $N\times N$ matrix; $\beta,\,\gamma\in C(\overline\Omega)$ with $\beta>0;\,q\in [0,\infty)$ and $\pan u$ is the conormal derivative of $u$ with respect to $A$: and everything is sufficiently regular. The solution of this well posed problem depends continuously on the ingredients of the problem, namely, $\A,\,\beta,\,\gamma,\,q,\, f.$ This is shown using semigroup methods in \cite{CFGGR}. More precisely, if we have a sequence of such problems with solutions $u_n$, and if $\A_n\to\A,\,\beta_n\to\beta,$ et al in a suitable sense, then $u_n\to u$, the solution of the limiting problem. The abstract analysis associated with operator semigroup theory gives this conclusion, but no rate of convergence. Determining how fast the convergence of the solutions is requires detailed estimates. Such estimates are provided in this paper.
Stability Estimates for Parabolic Problems with Wentzell boundary conditions / COCLITE G; GOLDSTEIN G.R; GOLDSTEIN J.A. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 245(2008), pp. 2595-2626.
Scheda prodotto non validato
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo
| Titolo: | Stability Estimates for Parabolic Problems with Wentzell boundary conditions |
| Autori: | |
| Data di pubblicazione: | 2008 |
| Rivista: | |
| Citazione: | Stability Estimates for Parabolic Problems with Wentzell boundary conditions / COCLITE G; GOLDSTEIN G.R; GOLDSTEIN J.A. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 245(2008), pp. 2595-2626. |
| Abstract: | Of concern is the uniformly parabolic problem \begin{equation*} u_t =\dv(\A\nabla u),\qquad u(0,x)=f(x),\qquad u_t +\beta\pan u+\gamma u-q\beta \lb u=0, \end{equation*} for $x\in \Omega\subset \R^N$ and $t\ge0$. Here $\A=\{a_{ij}(x)\}_{ij}$ is a real, hermitian, uniformly positive definite $N\times N$ matrix; $\beta,\,\gamma\in C(\overline\Omega)$ with $\beta>0;\,q\in [0,\infty)$ and $\pan u$ is the conormal derivative of $u$ with respect to $A$: and everything is sufficiently regular. The solution of this well posed problem depends continuously on the ingredients of the problem, namely, $\A,\,\beta,\,\gamma,\,q,\, f.$ This is shown using semigroup methods in \cite{CFGGR}. More precisely, if we have a sequence of such problems with solutions $u_n$, and if $\A_n\to\A,\,\beta_n\to\beta,$ et al in a suitable sense, then $u_n\to u$, the solution of the limiting problem. The abstract analysis associated with operator semigroup theory gives this conclusion, but no rate of convergence. Determining how fast the convergence of the solutions is requires detailed estimates. Such estimates are provided in this paper. |
| Handle: | http://hdl.handle.net/11586/15675 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
Copyright © 2020