Publications
Papers and preprints
A publication index organized by year and topic.
Global Existence, Invariant Region, and Enhanced Regularity for an Anisotropic Reaction-Diffusion Model of Myocardial Remodeling in Terms of Dirichlet Concentration Parameters
Zenodo preprint
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
On Global Solvability, Entropy Dissipation, and Numerical Analysis of Reaction-Diffusion Systems with Cross-Diffusion and Markov Kinetics
Zenodo preprint
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
On the Well-Posedness of Discrete Variational Problems with Edge-Aware Regularization
Modern Science: Theory and Practice
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