A framework of uniformly m-accretive operators in Lorentz spaces is built to apply the Crandall-Liggett theorem, yielding existence, uniqueness, stability of mild solutions to nonlinear parabolic equations with unbounded drift, with equivalence to weak solutions and long-time asymptotics.
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Well-posedness of nonlinear parabolic equations with unbounded drift via nonlinear evolution theory
A framework of uniformly m-accretive operators in Lorentz spaces is built to apply the Crandall-Liggett theorem, yielding existence, uniqueness, stability of mild solutions to nonlinear parabolic equations with unbounded drift, with equivalence to weak solutions and long-time asymptotics.