IJPAM: Volume 85, No. 2 (2013)
APPLICATIONS TO PROBLEMS WITH NONLINEAR
Institute for Analysis
Faculty of Mathematics and Sciences
Technical University Dresden
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
Download paper from here.
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