TY  - JOUR
ID  - Abdelouahab2024
LB  - Abdelouahab2024
AU  - Abdelouahab, Ahlem
AU  - Bensid, Sabri
TI  - Analysis of a multiphase free boundary problem
ST  - Analysis of a multiphase free boundary problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 5
SP  - 631
EP  - 649
DO  - https://doi.org/10.7494/OpMath.2024.44.5.631
UR  - https://doi.org/10.7494/OpMath.2024.44.5.631
AB  - 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.
KW  - discontinuous nonlinearity
KW  - free boundary
KW  - perturbation
KW  - tumor growth
SN  - 1232-9274
ER  -