Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1117.65077
Ashyralyev, Allaberen
Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces. (English)
[J] J. Evol. Equ. 6, No. 1, 1-28 (2006). ISSN 1424-3199; ISSN 1424-3202/e

The author consider an abstract parabolic equation $v'(t)+A v(t)=f(t)$ where the initial condition is replaced by the nonlocal condition $v(0)=v(\lambda)+\mu$. All variables and constants takes values in a Hilbert space $E$ and $A$ is a linear and possible unbounded operator on this space. Under the assumption that the operator $-A$ generates an analytic semigroup $\{\exp(-At)\}_{t\geq0}$ with exponential decay, it is shown that the solutions to the nonlocal parabolic equation satify a coercivity estimate in terms of $f$ and $\mu$ with the implication that the problem is well-posed. In addition, first and second order difference schemes are given and so called almost coercive inequalities are established for these (the multiplier in the inequality contains the factor $\min\{1/\tau,\vert \ln \Vert A\Vert _{E\to E}\vert \}$, where $\tau$ is the time step).
[Stefan Jakobsson (Göteborg)]

MSC 2000:: *65J10 Equations with linear operators (numerical methods)
65M06 Finite difference methods (IVP of PDE)
65L05 Initial value problems for ODE (numerical methods)
47D06 One-parameter semigroups and linear evolution equations
34G10 Linear ODE in abstract spaces
35K90 Abstract parabolic evolution equations

Keywords: difference schemes; well-posedness; coercive inequalities; abstract parabolic equation; Hilbert space

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]