It is well known that the uniqueness backward in time for smooth solutions to a linear parabolic equation is an improperly posed problem. On the other hand, for the p-laplacian parabolic problem, p in (1,2), the extinction of the solution in a finite interval of time is one of the major property. In this note we investigate on the extinction property in the case of an electrorheological fluid. In the L2-setting of weak solutions we are able to prove the following characterization: there is extinction of a solution to p(x)-Stokes IBVP iff p(x)\in[2n/(n+2),2).
Electrorheological fluids: Ill posedness of uniqueness backward in time
Abbatiello, A.;Crispo, F.;Maremonti, P.
2018
Abstract
It is well known that the uniqueness backward in time for smooth solutions to a linear parabolic equation is an improperly posed problem. On the other hand, for the p-laplacian parabolic problem, p in (1,2), the extinction of the solution in a finite interval of time is one of the major property. In this note we investigate on the extinction property in the case of an electrorheological fluid. In the L2-setting of weak solutions we are able to prove the following characterization: there is extinction of a solution to p(x)-Stokes IBVP iff p(x)\in[2n/(n+2),2).File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
