On multivalued evolution equations in Hilbert spaces |
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Authors: | H Attouch A Damlamian |
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Institution: | (1) Institute de Mathématiques, Université Paris-Sud Centre d’Orsay, 91 Orsay, France |
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Abstract: | The Cauchy problemdu/dt+Au+B(t,u)∋0,u(0)=u
0 is studied in a separable Hilbert space setting, whenA is a multivalued maximal monotone operator, andB is a multivalued operator which is measurable with respect to the time variable and upper semi-continuous with respect to
the space variable. Under some boundedness conditions onB, an existence theorem is proved, with the extra assumption, in the infinite dimensional case thatA is the subdifferential of a proper lower semi-continuous inf-compact convex function. A theorem of dependence upon the initial
condition is also given. |
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Keywords: | |
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