Regularity of solutions to a free boundary problem modeling tumor growth by Stokes equation |
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Authors: | Fujun Zhou Junde Wu |
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Affiliation: | a Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, PR China b Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, PR China |
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Abstract: | In this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid-like tissues. The model equations include a quasi-stationary diffusion equation for the nutrient concentration, and a Stokes equation with a source representing the proliferation density of the tumor cells, subject to a boundary condition with stress tensor effected by surface tension. This problem is a fully nonlinear problem involving nonlocal terms. Based on the employment of the functional analytic method and the theory of maximal regularity, we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity. |
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Keywords: | Free boundary problem Tumor growth model Regularity Analyticity |
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