Mechanochemical Pattern Formation in a Morphogen-Coupled Tissue Plate: Well-Posedness, Instability Thresholds, and Nonlinear Dynamics
This paper establishes the well-posedness of a mechanochemical plate-diffusion model coupling tissue deformation and morphogen concentration, and through spectral analysis, demonstrates that the sign of deformation-to-morphogen feedback critically determines the stability of the homogeneous state, thereby identifying the linear instability mechanisms that precede nonlinear pattern formation.