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On a class of doubly nonlinear evolution equations. (English) Zbl 0707.34053
Summary: The abstract equation A du/dt\(+Bu\ni f\) is considered for A and B nonlinear maximal monotone operators in a Hilbert space H, with A bounded, B unbounded and such that its domain D(B) is contained in a Banach space V compactly embedded in H. Existence results are proved for the related initial-value problem, requiring that either A or B be the subdifferential of a convex and lower semicontinuous function, and assuming suitable coerciveness conditions. Arguments are based on monotonicity and compactness techniques.

MSC:
34G20 Nonlinear differential equations in abstract spaces
35K55 Nonlinear parabolic equations
35G25 Initial value problems for nonlinear higher-order PDEs
47H20 Semigroups of nonlinear operators
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