AI 中文总结
该研究针对趋化性输运的爱因斯坦型物质平衡模型，分析行波解，证明输运主导区相干行波带的存在性，推导扰动界并将系统约化为三阶常微分方程，适用于油气藏形成等问题。
AI 中文摘要
我们构建了一个非线性连续介质输运模型，用于描述耦合两相介质中局域行波结构的形成。该模型源于爱因斯坦型物质平衡公式，其中位移由扩散及依赖背景的输运机制的梯度共同产生。所得系统耦合了扩散、非线性梯度驱动输运与背景相的耗散。所提框架适用于一般趋化性输运，尤其适用于油气藏形成相关问题。我们分析了行波解，确立了输运主导区域中相干行波带的存在性：对于任意给定参考时间，流动相形成唯一的单峰分布，而背景组分在渐近状态间呈现正的、有界的单调逻辑型转变；得到了行波分布的显式表达式，并证明其平移意义下的唯一性。我们进一步推导了行波带附近的线性化扰动算子，通过最大值原理论证确立了有限时间扰动界。最后，将行波系统约化为背景分布的非线性三阶常微分方程，提供了相干结构的另一种表征方式。
英文摘要
We develop a nonlinear continuum transport model for localized traveling structures in a coupled two-phase medium. The model is derived from an Einstein-type material-balance formulation combining diffusion with directed transport induced by the relative gradient of an evolving background phase. The resulting system couples diffusion, nonlinear gradient-driven transport, and irreversible background depletion. The framework provides a mathematical model for chemotactic transport and a possible modeling perspective for processes associated with the formation of oil and gas deposits. We analyze traveling-wave solutions and identify beta = chi/D = 1 as the critical threshold for globally positive localized traveling bands under prescribed asymptotic conditions as the traveling coordinate s tends to plus or minus infinity. Such bands exist for beta greater than or equal to 1, whereas for 0 < beta < 1 the positive branch reaches zero background concentration at a finite traveling coordinate. For beta greater than or equal to 1, explicit profiles are obtained and, for fixed wave speed c > 0 and right-end state V_plus > 0, are unique up to spatial translation in the traveling coordinate s. We further derive the variable-coefficient linearized perturbation operator and establish a conditional finite-time a priori estimate for the mobile-phase perturbation under bounded background forcing using a maximum-principle argument.
Comments37 pages, 1 figure
