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We derive a model for the non-isothermal reaction-diffusion equation.Combining ideas from non-equilibrium thermodynamics with the energeticvariational approach we obtain a general system modeling the evolution of anon-isothermal chemical reaction with general mass kinetics. From this werecover a linearized model for a system close to equilibrium and we analyze theglobal-in-time well-posedness of the system for small initial data for acritical Besov space.

Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space