caa a22 4500 445843470 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00526-010-0342-2 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0342-2 Vergara Vicente Instituto de Alta Investigación, Universidad de Tarapacá, Antofagasta N. 1520, Arica, Chile aut Convergence to steady states of solutions to nonlinear integral evolution equations [Elektronische Daten] [Vicente Vergara] We prove that any global bounded solution of the nonlinear evolutionary integral equation $$\dot{u}(t) + \int\limits_0^t a(t-s)\mathcal{E}'(u(s))ds =f(t), \quad t >0 $$tends to a single equilibrium state for long time (i.e., $${\mathcal{E}'(\vartheta)=0}$$ where $${\vartheta= \lim_{t \rightarrow \infty} u(t)}$$ on a real Hilbert space), where $${\mathcal{E}'}$$ is the Fréchet derivative of a functional $${\mathcal{E}}$$, which satisfies the Łojasiewicz-Simon inequality near $${\vartheta}$$. The vector-valued function f and the scalar kernel a satisfy suitable conditions. Springer-Verlag, 2010 Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 319-334 0944-2669 40:3-4<319 2011 40 526 https://doi.org/10.1007/s00526-010-0342-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0342-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vergara Vicente Instituto de Alta Investigación, Universidad de Tarapacá, Antofagasta N. 1520, Arica, Chile aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 319-334 0944-2669 40:3-4<319 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer