WELL-POSEDNESS AND LONG-TIME BEHAVIOR FOR A CLASS OF DOUBLY NONLINEAR EQUATIONS

By Giulio Schimperna, Antonio Segatti, Ulisse Stefanelli. 2006

48 citations recorded by the source corpus.

This paper addresses a doubly nonlinear parabolic inclusion of the form $\mathcal A (u_t)+\mathcal B (u)$ ∋ f. Existence of a solution is proved under suitable monotonicity, coercivity, and structure assumptions on the operators $\mathcal A $ and $\mathcal B$, which in particular are both supposed to be subdifferentials of functionals on $L^2(\Omega)$. Since unbounded operators $\mathcal A $ are included in the analysis, this theory partly extends Colli & Visintin's work [24]. Moreover, under additional hypotheses on $\mathcal B$, 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/f34597c74a54f0c34626706c0d48e4b529592af3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Nonsmooth analysis of doubly nonlinear evolution equations (2011, background): “10) which has been exploited in [51] to prove well-posedness (for the Cauchy problem) for the gradient system (V,E,Ψ, ∂E), and existence of the global attractor for the related dynamical system.”
A metric approach to a class of doubly nonlinear evolution equations and applications (2008, background): “We recall that, in the same setting, long-time behavior results for (DNE) have recently been obtained in [48, 47].”