Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 0801.65135
Thomée, Vidar; Wahlbin, Lars B.
Long-time numerical solution of a parabolic equation with memory. (English)
[J] Math. Comput. 62, No.206, 477-496 (1994). ISSN 0025-5718; ISSN 1088-6842/e

The stability of temporal discretization is investigated for integral equations of the form $\partial\sb t u + Au = \int\sp t\sb 0 b(t - s) Bu(s) ds + f(t)$, where $\partial\sb t + A$ is a parabolic operator on a Hilbert space. The principal question is whether or not solutions remain bounded as $t \to \infty$. The method of analysis is by energy inequalities, but for the special case $B = A$ more detailed results are obtained from eigenfunction expansions. The question of quadrature schemes for the integral operator is also discussed.
[G.Hedstrom (Livermore)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45K05 Integro-partial differential equations
45N05 Integral equations in abstract spaces

Keywords: long-time numerical solution; parabolic equation with memory; stability; Hilbert space; energy inequalities; eigenfunction expansions; quadrature schemes

Cited in: Zbl 0958.45004

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]