Publications

Papers and preprints

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2026

Global Existence, Invariant Region, and Enhanced Regularity for an Anisotropic Reaction-Diffusion Model of Myocardial Remodeling in Terms of Dirichlet Concentration Parameters

Zenodo preprint

Evgeny Yuryevich Shchetinin, Andrey Andreyevich Shevchuk

A multicomponent anisotropic reaction-diffusion model for post-infarction myocardial remodeling is formulated in terms of Dirichlet concentration parameters so that composition and uncertainty are represented together. The paper proves global existence, establishes invariant-region bounds, and derives enhanced regularity and short-time unconditional uniqueness under additional assumptions.

  • Nonlinear PDEs
  • Applied Systems

DOI10.5281/zenodo.19636807

2026

On Global Solvability, Entropy Dissipation, and Numerical Analysis of Reaction-Diffusion Systems with Cross-Diffusion and Markov Kinetics

Zenodo preprint

Evgeny Yuryevich Shchetinin, Andrey Andreyevich Shevchuk

This paper studies multicomponent reaction-diffusion systems with cross-diffusion and Markov kinetics in an entropy-structured setting. It establishes global weak solvability for an admissible class, proves exponential relaxation in the conservative regime, and combines theory with entropy-consistent numerical experiments.

  • Nonlinear PDEs
  • Numerical Methods

DOI10.5281/zenodo.19635808

2026

On the Well-Posedness of Discrete Variational Problems with Edge-Aware Regularization

Modern Science: Theory and Practice

Evgeny Yuryevich Shchetinin, Andrey Andreyevich Shevchuk

This article analyzes why standard edge-aware weights collapse to isotropic behavior under grid refinement. It introduces a scale-consistent formulation based on normalized directional differences and proves convergence to a nontrivial weighted anisotropic Dirichlet energy, supported by numerical validation on synthetic and cardiac MRI data.

  • Nonlinear PDEs
  • Numerical Methods

DOI10.34660/INF.2026.79.37.103