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In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model. 相似文献
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Phan Quoc Khanh 《Numerical Functional Analysis & Optimization》2018,39(1):100-125
We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations. 相似文献
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Shai Shechter 《Journal of Pure and Applied Algebra》2019,223(10):4384-4425
Let be a complete discrete valuation ring with finite residue field of odd characteristic, and let G be a symplectic or special orthogonal group scheme over . For any let denote the ?-th principal congruence subgroup of . An irreducible character of the group is said to be regular if it is trivial on a subgroup for some ?, and if its restriction to consists of characters of minimal -stabilizer dimension. In the present paper we consider the regular characters of such classical groups over , and construct and enumerate all regular characters of , when the characteristic of is greater than two. As a result, we compute the regular part of their representation zeta function. 相似文献
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