Glasnik matematički, Vol. 53 No. 2, 2018.
Original scientific paper
https://doi.org/10.3336/gm.53.2.13
On the existence of a solution of a class of non-stationary free boundary problems
Mahmoud Bousselsal
; Department of Mathematics, Labo. Part. Diff. Eq. & Hist. Maths, Ecole Normale Supérieure, 16050 Vieux-Kouba Algiers, Algeria
Abdeslem Lyaghfouri
; Department of Mathematics and Natural Sciences, American University of Ras Al Khaimah, Ras Al Khaimah, UAE
Elmehdi Zaouche
; Department of Mathematics, Labo. Oper. Theo. & Part. Diff. Eq.: Foundations and Applications, University of EL Oued, B. P. 789 El Oued 39000, Algeria
Abstract
We consider a class of parabolic free boundary problems with heterogeneous coefficients including, from a physical point of view, the evolutionary dam problem. We establish existence of a solution for this problem. We use a regularized problem for which we prove existence of a solution by applying the Tychonoff fixed point theorem. Then we pass to the limit to get a solution of our problem. We also give a regularity result of the solutions.
Keywords
Parabolic free boundary problems; evolution dam problem; existence; regularity
Hrčak ID:
214484
URI
Publication date:
30.12.2018.
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