Monobe, Harunori Behavior of solutions for a free boundary problem describing amoeba motion. (English) Zbl 1249.35357 Differ. Integral Equ. 25, No. 1-2, 93-116 (2012). 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. Cited in 2 ReviewsCited in 3 Documents MSC: 35R35 Free boundary problems for PDEs 35A09 Classical solutions to PDEs 45K05 Integro-partial differential equations Keywords:free boundary problem; amoeba motion; spherically symmetric solution; boundedness; Hölder norm PDF BibTeX XML Cite \textit{H. Monobe}, Differ. Integral Equ. 25, No. 1--2, 93--116 (2012; Zbl 1249.35357)