@article{1437144,
      author = {Yagi, Atsushi,},
      url = {http://library.usi.edu/record/1437144},
      title = {Abstract Parabolic Evolution Equations and  Łojasiewicz-Simon Inequality I : Abstract Theory /},
      abstract = {The classical Łojasiewicz gradient inequality (1963) was  extended by Simon (1983) to the infinite-dimensional  setting, now called the Łojasiewicz-Simon gradient  inequality. This book presents a unified method to show  asymptotic convergence of solutions to a stationary  solution for abstract parabolic evolution equations of the  gradient form by utilizing this Łojasiewicz-Simon gradient  inequality. In order to apply the abstract results to a  wider class of concrete nonlinear parabolic equations, the  usual Łojasiewicz-Simon inequality is extended, which is  published here for the first time. In the second version,  these abstract results are applied to reaction-diffusion  equations with discontinuous coefficients,  reaction-diffusion systems, and epitaxial growth equations.  The results are also applied to the famous chemotaxis  model, i.e., the Keller-Segel equations even for  higher-dimensional ones.},
      doi = {https://doi.org/10.1007/978-981-16-1896-3},
      recid = {1437144},
      pages = {1 online resource (68 pages)},
}