We discuss singular time dependent absorption-excitation rates for second order parabolic equations. A suitable class, the non-autonomous Kato class, is defined for the heat equation in connection with the non-autonomous Miyadera perturbation theorem. We give sufficient conditions in terms of integrability for a potential to belong to the non-autonomous Kato class.
KeywordsParabolic Equation Kato Heat Equation Suitable Class Perturbation Theorem
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