Differential and Integral Equations
- Differential Integral Equations
- Volume 25, Number 1/2 (2012), 93-116.
Behavior of solutions for a free boundary problem describing amoeba motion
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.
Differential Integral Equations, Volume 25, Number 1/2 (2012), 93-116.
First available in Project Euclid: 20 December 2012
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Monobe, Harunori. Behavior of solutions for a free boundary problem describing amoeba motion. Differential Integral Equations 25 (2012), no. 1/2, 93--116. https://projecteuclid.org/euclid.die/1356012828