Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues
DOI:
https://doi.org/10.71310/pcam.2_72.2026.02Keywords:
Green’s function, potential, Jordan arc, mixed type equation, Lipschitz condition, biomedicine, oncology, tumor, anisotropyAbstract
This paper examines a boundary value problem for a degenerate elliptic equation in a planar domain bounded by a line segment and an analytic curve. The primary objective is to construct an explicit analytical solution using the Green’s function together with singleand double-layer potential methods. A rigorous proof of the existence and uniqueness of the solution under mixed boundary conditions is presented. The degeneracy on a portion of the boundary introduces significant analytical difficulties, necessitating the use of advanced techniques in the theory of elliptic equations with singular coefficients. Furthermore, the potential applications of the model in biomedical settings, particularly in oncology, are discussed. The equation captures anomalous diffusion processes in tumor tissues, incorporating the spatial heterogeneity of the medium. This makes the model a valuable tool for analyzing the distribution of drugs, oxygen, and other substances in biological structures characterized by pronounced anisotropy and heterogeneity.
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