Opuscula Math. 44, no. 5 (2024), 631-649
https://doi.org/10.7494/OpMath.2024.44.5.631
Opuscula Mathematica
Analysis of a multiphase free boundary problem
Ahlem Abdelouahab
Sabri Bensid
Abstract. In this paper, we investigate a free boundary problem relevant in several applications, such as tumor growth models. Our problem is expressed as an elliptic equation involving discontinuous nonlinearities in a specified domain with a moving boundary. We establish the existence and uniqueness of solutions and provide a qualitative analysis of the free boundaries generated by the nonlinear term (inner boundaries). Furthermore, we analyze the dynamics of the outer region boundary. The final result demonstrates that under certain conditions, our problem is solvable in the neighborhood of a radial solution.
Keywords: discontinuous nonlinearity, free boundary, perturbation, tumor growth.
Mathematics Subject Classification: 34R35, 35J25, 92B05, 35R35.
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- Ahlem Abdelouahab
- University of Tlemcen, Faculty of Sciences, Department of Mathematics, Dynamical Systems and Applications Laboratory, B.P. 119, Tlemcen 13000, Algeria
- Sabri Bensid (corresponding author)
- University of Tlemcen, Faculty of Sciences, Department of Mathematics, Dynamical Systems and Applications Laboratory, B.P. 119, Tlemcen 13000, Algeria
- Communicated by J.I. Díaz.
- Received: 2023-12-21.
- Revised: 2024-04-20.
- Accepted: 2024-05-10.
- Published online: 2024-07-01.
