In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

Using the technique developed by F. John in 7], we study the existence and the nonexistence of global classical solutions to the Cauchy problem for @ 2 t u ? x u = jvj p ; @ 2 t v ? x v = juj q ; in R 3 x 0; +1.

We prove global existence for a simplified model of one-dimensional thermoelasticity. The governing equations satisfy the balance of momentum and a modified energy balance. The application we wish to study by investigating this model are shapememory alloys. They are a prominent example of solids undergoing structural phase transitions. A characteristic feature of these materials is that several...

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.