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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.

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
Full Text: DOI
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