In this paper, we present a detailed study of class sixth-order semilinear PDEs: existence, regularity and uniqueness. The uniqueness results are consequence maximum principle called the P-function method.

The hard problem of consciousness has been often claimed to be unsolvable by the methods of traditional empirical sciences. It has been argued that all the objects of empirical sciences can be fully analyzed in structural terms but that consciousness is (or has) something over and above its structure. However, modern neuroscience has introduced a theoretical framework in which also the apparent...

We use functional calculus methods to investigate qualitative properties of C0semigroups that are preserved by time-discretization methods. Preservation of positivity, concavity and other qualitative shape properties which can be described via positivity are treated in a Banach lattice framework. Preservation of contractivity (or norm-bound) of the semigroup is investigated in the Banach space ...