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首页> 外文期刊>Dynamic Systems and Applications >LONG-TIME BEHAVIOR OF SOLUTIONS OF A NONLINEAR DIFFUSION MODEL WITH TRANSMISSION BOUNDARY CONDITIONS
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LONG-TIME BEHAVIOR OF SOLUTIONS OF A NONLINEAR DIFFUSION MODEL WITH TRANSMISSION BOUNDARY CONDITIONS

机译：传输边界条件的非线性扩散模型解的长时间行为

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摘要

In order to accurately simulate the transport of growth factor from tumor site into a nearby capillary wall, a recently introduced model of tumor-induced capillary growth incorporates a new form of transmission boundary flux. Growth factor emitted from the tumor may be viewed as a diffusible chemical moving through intersticial space, which is represented as a porous medium. Transmission between the capillary wall and intersticial space gives rise to a type of continuous delay/memory condition at the boundary. Herein, we establish results on global solvability and blow up in finite time for a general nonlinear diffusion model, including such transmission boundary conditions. Although the model appears more closely aligned with models involving nonlinear flux conditions at the boundary, these results bear notable similarities to those with Dirichlet boundary conditions.
机译：为了准确模拟生长因子从肿瘤部位到附近毛细血管壁的转运，最近引入的肿瘤诱导毛细血管生长模型结合了一种新型的传输边界通量。从肿瘤中散发出来的生长因子可被视为通过间隙空间传播的可扩散化学物质，其表现为多孔介质。毛细管壁和间隙空间之间的传输会在边界处产生一种连续的延迟/内存条件。在这里，我们建立了关于整体可解性的结果，并在有限的时间内爆炸了一个通用的非线性扩散模型，包括这种传输边界条件。尽管该模型看起来与边界上涉及非线性通量条件的模型更加一致，但这些结果与Dirichlet边界条件下的结果具有显着相似性。

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