On a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-05-30 DOI:10.1016/j.nonrwa.2025.104419

Giulia Cavalleri , Pierluigi Colli , Alain Miranville , Elisabetta Rocca

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引用次数: 0

Abstract

In this paper, we study a nonlinearly coupled initial–boundary value problem describing the evolution of brain tumor growth, including lactate metabolism. In our modeling approach, we also take into account the viscoelastic properties of the tissues as well as the reversible damage effects that could occur, possibly caused by surgery. After introducing the PDE system, coupling a Fischer–Kolmogorov type equation for the tumor phase with a reaction–diffusion equation for the lactate, a quasi-static momentum balance with nonlinear elasticity and viscosity matrices, and a nonlinear differential inclusion for the damage, we prove the existence of global in time weak solutions under reasonable assumptions on the involved functions and data. Strengthening these assumptions, we subsequently prove further regularity properties of the solutions as well as their continuous dependence with respect to the data, entailing the well-posedness of the Cauchy problem associated with the nonlinear PDE system.

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具有乳酸代谢、粘弹性效应和组织损伤的脑肿瘤生长模型

本文研究了一个描述脑肿瘤生长演化的非线性耦合初边值问题，包括乳酸代谢问题。在我们的建模方法中，我们还考虑了组织的粘弹性特性以及可能发生的可逆损伤效应，可能由手术引起。引入PDE系统，将肿瘤相的fisher - kolmogorov型方程与乳酸相的反应扩散方程耦合，将非线性弹性和黏度矩阵的准静态动量平衡和损伤的非线性微分包涵耦合，在合理的函数和数据假设下证明了整体时间弱解的存在性。加强这些假设，我们随后进一步证明了解的正则性及其对数据的连续依赖性，从而得到与非线性PDE系统相关的柯西问题的适定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.