Asymptotic Blow-Up Profiles and Renormalized Entropy Solutions for Degenerate Parabolic Systems with Non-Local Integro-Differential Coupling in Hyper-Arrhenius Stellar Ignition

Mathematical Applications of Science Fiction We present an analytical framework for a class of degenerate parabolic systems with non-local integro-differential coupling, motivated by Hyper-Arrhenius stellar ignition in high-density plasmas. We study the evolution of the system under nonlinear diffusion and fractional operators, and prove the existence of renormalized entropy solutions for initial data in critical function spaces. We analyze the blow-up behavior near finite-time singularities using rescaled coordinates and spectral analysis of the linearized operator. The solutions converge to self-similar profiles corresponding to specific topological solitons. Additionally, we provide key lemmas on commutator estimates for fractional operators and establish a Liouville-type theorem for the limiting parabolic equation.