Behavior of solutions for a free boundary problem describing amoeba motion. (English) Zbl 1249.35357

Summary: In this paper we consider a free boundary problem (a modified Umeda’s model) related to amoeba motion. We show the existence of time-global classical solutions and study their behavior in the spherically symmetric case. To this end, we carefully trace the trajectory of solutions, and find a positive invariant region to show the boundedness of solutions. We observe that the properties of the solutions agree with the real motion of amoeba.


35R35 Free boundary problems for PDEs
35A09 Classical solutions to PDEs
45K05 Integro-partial differential equations