Abstract
AbstractThe final value value problem for the Brinkman–Forchheimer–Kelvin–Voigt equations is analysed for quadratic and cubic types of Forchheimer nonlinearity. The main term in the Forchheimer equations is allowed to be fully anisotropic. It is shown that the solution depends continuously on the final data provided the solution satisfies an a priori bound in $$L^3.$$
L
3
.
The technique employed avoids the use of a specialist method for an improperly posed problem such as logarithmic convexity.
Funder
Università degli Studi di Napoli Federico II
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Computational Mechanics
Reference46 articles.
1. Agmon, S.: Unicité et convexité dans les problèmes différentiels. In: Sem. Math. Sup, University of Montreal Press (1966)
2. Agmon, S., Nirenberg, L.: Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space. Commun. Pure Appl. Math. 20, 207–229 (1967)
3. Ames, K.A., Epperson, J.F.: A kernel based method for the approximate soluition of backward parabolic problems. SIAM J. Numer. Anal. 34, 1357–1390 (1997)
4. Ames, K.A., Straughan, B.: Non-standard and Improperly Posed Problems. Academic Press, Cambridge (1997)
5. Ames, K.A., Clark, G.W., Epperson, J.F., Oppenheimer, S.F.: A comparison of regularizations for an ill posed problem. Math. Comput. 34, 1451–1471 (1998)
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