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Abstract:
This study investigates the regulation of tissue growth through mathematical modeling of systemic and local feedback mechanisms. Employing reaction-diffusion equations, the models explore the dynamics of tissue growth, emphasizing endocrine signaling and inter-tissue communication. The analysis identifies critical factors influencing the emergence of spatial structures, bifurcation phenomena, the existence and stability of stationary pulse and wave solutions. It also elucidates mechanisms for achieving coordinated tissue growth. In particular, if negative feedback is sufficiently strong, their final finite size is provided by a stable pulse, otherwise they manifest unlimited growth in the form of a wave. These findings contribute to the theoretical insights into biological processes such as embryogenesis, regeneration, and tumor development, while highlighting the role of feedback systems in maintaining physiological homeostasis.