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.
|Number of pages||24|
|Journal||Differential and Integral Equations|
|Publication status||Published - Jan 1 2012|
ASJC Scopus subject areas
- Applied Mathematics