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On some doubly nonlinear evolution equations in Banach spaces

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Abstract

The initial value problem is studied for the abstract evolution equationA(du/dt)+B(u) ∋f, whereA andB are maximal monotone operators from a Banach spaceW to its dual spaceW *, withA bounded andB unbounded. Assuming suitable coerciveness conditions, the existence of a solution is established when at least one of the operators is the subdifferential of a proper convex lower semicontinuous function. The existence theorems are shown by introducing a suitable time discretization of the problem and then passing to the limit by monotonicity and compactness. Uniqueness is proved whenA orB is linear and symmetric and one of them is strictly monotone. Applications are indicated for classes of nonlinear partial differential equations and systems.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pavia, Strada Nuova 65, 27100, Pavia, Italy

    Pierluigi Colli

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  1. Pierluigi Colli
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Additional information

This work has been supported by M.U.R.S.T. (fondi per la ricerca scientifica) and by theIstituto di Analisi Numerica of C.N.R., Pavia, Italy.

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Colli, P. On some doubly nonlinear evolution equations in Banach spaces. Japan J. Indust. Appl. Math. 9, 181 (1992). https://doi.org/10.1007/BF03167565

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  • DOI: https://doi.org/10.1007/BF03167565

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