The final 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 isotropic. It is shown that the solution depends continuously on the final data provided the solution satisfies an a priori bound in L^3. The technique employed avoids the use of a specialist method for an improperly posed problem as logarithmic convexity.
Stabilization estimates for Brinkman-Forchheimer-Kelvin-Voigt equation backward in time / Gentile, Maurizio; Straughan, Brian. - In: ACTA MECHANICA. - ISSN 0001-5970. - 234:(2023), pp. 4001-4009. [10.1007/s00707-023-03592-5]
Stabilization estimates for Brinkman-Forchheimer-Kelvin-Voigt equation backward in time
Maurizio Gentile
;
2023
Abstract
The final 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 isotropic. It is shown that the solution depends continuously on the final data provided the solution satisfies an a priori bound in L^3. The technique employed avoids the use of a specialist method for an improperly posed problem as logarithmic convexity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
