Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities

IF 0.6 4区数学 Q3 MATHEMATICS

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2021-04-01 DOI:10.4171/rlm/969

P. Colli, G. Gilardi, J. Sprekels

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Abstract

This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et al., Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects, Math. Models Methods Appl. Sci. 30 (2020), 1253–1295]). The related system includes two evolutionary operator equations involving fractional powers of selfadjoint, nonnegative, unbounded linear operators having compact resolvents. Both equations contain nonlinearities and in particular the equation describing the dynamics of the tumor phase variable has the structure of a Allen–Cahn equation with double-well potential and additional nonlinearity depending also on the other variable, which represents the nutrient concentration. The equation for the nutrient concentration is nonlinear as well, with a term coupling both variables. For this system we design an existence, uniqueness and continuous dependence theory by setting up a careful analysis which

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一类用分数算子和一般非线性模拟前列腺癌症生长的相场系统的平稳性

本文讨论了最近引入和分析的前列腺癌症生长与化疗和抗血管生成治疗的数学模型产生的一般方程组和条件（见[P.Colli等人，具有化疗和抗血管生成治疗效果的前列腺癌症生长相场模型的数学分析和模拟研究，数学模型方法应用科学30（2020），1253–1295]）。相关系统包括两个演化算子方程，涉及具有紧致预解的自伴、非负、无界线性算子的分数次幂。这两个方程都包含非线性，特别是描述肿瘤期变量动力学的方程具有Allen–Cahn方程的结构，该方程具有双井电位和额外的非线性，也取决于代表营养浓度的另一个变量。营养物浓度的方程也是非线性的，有一个耦合两个变量的项。对于这个系统，我们通过仔细的分析，设计了一个存在性、唯一性和连续依赖性理论

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来源期刊

Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.