IJPAM: Volume 85, No. 2 (2013)

AUTONOMOUS EVOLUTIONARY INCLUSIONS WITH
APPLICATIONS TO PROBLEMS WITH NONLINEAR
BOUNDARY CONDITIONS

Sascha Trostorff
Institute for Analysis
Faculty of Mathematics and Sciences
Technical University Dresden
Dresden, GERMANY


Abstract. We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the well-posedness relies on a well-known perturbation result for maximal monotone operators. Moreover, we show that certain types of nonlinear boundary value problems are covered by this class of inclusions and we derive necessary conditions on the operators on the boundary in order to apply the solution theory. We exemplify our findings by two examples.

Received: December 11, 2012

AMS Subject Classification: 34G25, 35F30, 35R20, 46N20, 47J35

Key Words and Phrases: evolutionary inclusions, well-posedness, causality, maximal monotonicity, impedance type boundary conditions, frictional boundary conditions

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DOI: 10.12732/ijpam.v85i2.10 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 2