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In the study of mathematical models that arise in the context of concrete plications, the following two questions are of fundamental importance: (i) we posedness of the model, including existence and uniqueness of solutions; and (ii) qualitative properties of solutions. A positive answer to the ?rst question, ing of prime interest on purely mathematical grounds, also provides an important test of the viability of the model as a description of a given physical phenomenon. An answer or insight to the second question provides a wealth of information about the model, hence about the process it describes. Of particular interest are questions related to longtime behavior of solutions. Such an evolution property cannot be v i?ed empirically, thus any in apriori information about the longtime asymptotics can be used in predicting an ultimate longtime response and dynamical behavior of solutions. In recent years, this set of investigations has attracted a great deal of attention. Consequent efforts have then resulted in the creation and infusion of new methods and new tools that have been responsible for carrying out a successful an ysis of longtime behavior of several classes of nonlinear PDEs.
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