Well-posedness and long-time behavior for a class of doubly nonlinear equations

Details Well-posedness and long-time behavior for a class of doubly nonlinear equations Well-posedness and long-time behavior for a class of doubly nonlinear equations

2006-11-03

arxiv.org/abs/math/0611071v1

Mathematics

Analysis of PDEs

Scientific paper

This paper addresses a doubly nonlinear parabolic inclusion of the form $A(u_t)+B(u)\ni f$. Existence of a solution is proved under suitable monotonicity, coercivity, and structure assumptions on the operators $A$ and $B$, which in particular are both supposed to be subdifferentials of functionals on $L^2(\Omega)$. Moreover, under additional hypotheses on $B$, uniqueness of the solution is proved. Finally, a characterization of $\omega$-limit sets of solutions is given and we investigate the convergence of trajectories to limit points.

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