Abstract.
It is shown that a special case of the well-known Lojasiewicz gradient inequality is sufficient to give a unified background for many convergence results in gradient or gradient-like systems appearing previously in the Literature. Besides as an illustration we give a direct proof of convergence in the case of 1D wave equations by a suitable adaptation of Zelenyak’s method.
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Haraux, A., Jendoubi, M.A. On the convergence of global and bounded solutions of some evolution equations. J. evol. equ. 7, 449–470 (2007). https://doi.org/10.1007/s00028-007-0297-8
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DOI: https://doi.org/10.1007/s00028-007-0297-8