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Well-posedness and stability of a multi-dimensional tumor growth model. (English) Zbl 1161.35058

Summary: We study a moving boundary problem modeling the growth of in vitro tumors. This problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure, respectively, and a first-order partial differential equation describing the evolution of the moving boundary. An important feature is that the effect of surface tension on the moving boundary is taken into account. We show that this problem is locally well-posed for a large class of initial data by using analytic semi-group theory. We also prove that if the surface tension coefficient \(\gamma\) is larger than a threshold value \(\gamma_*\) then the unique flat equilibrium is asymptotically stable, whereas in the case \(\gamma < \gamma_*\) this flat equilibrium is unstable.

MSC:

35R35 Free boundary problems for PDEs
35Q80 Applications of PDE in areas other than physics (MSC2000)
35B35 Stability in context of PDEs
92C10 Biomechanics
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