Differential and Integral Equations

Behavior of solutions for a free boundary problem describing amoeba motion

Harunori Monobe

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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.

Article information

Differential Integral Equations, Volume 25, Number 1/2 (2012), 93-116.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems 35A09: Classical solutions 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]


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

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