This second volume continues the study on asymptotic convergence of global solutions of
parabolic equations to stationary solutions by utilizing the theory of abstract parabolic
evolution equations and the Lojasiewicz-Simon gradient inequality. In the first volume of the
same title after setting the abstract frameworks of arguments a general convergence theorem
was proved under the four structural assumptions of critical condition Lyapunov function
angle condition and gradient inequality. In this volume with those abstract results reviewed
briefly their applications to concrete parabolic equations are described.Chapter 3 presents a
discussion of semilinear parabolic equations of second order in general n-dimensional spaces
and Chapter 4 is devoted to treating epitaxial growth equations of fourth order which
incorporate general roughening functions. In Chapter 5 consideration is given to the
Keller-Segel equations in one- two- and three-dimensional spaces. Some of these results had
already been obtained and published by the author in collaboration with his colleagues. However
by means of the abstract theory described in the first volume those results can be extended
much more.Readers of this monograph should have a standard-level knowledge of functional
analysis and of function spaces. Familiarity with functional analytic methods for partial
differential equations is also assumed.
