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This paper will be organized as follows: in Section 2, we shall give some preliminaries; in Section 3, the existence and uniqueness of global weak and strong solutions will be derived; we shall prove the existence of a uniform pullback absorbing ball in Section 4; with the pullback attractors we will conclude in the last section.

For showing the deeper meaning of several results derived this way, we shall make use, however, of different rather technical systems of coordinates which will be introduced in later sections.

To derive our conclusion, we shall use some ideas of [3].

Applying Lemmas 2.5 and 2.6 and the results derived for step mappings in Section 3, we shall derive in this section criteria for HK, HL, Bochner and Riemann integrability of right regulated mappings.

To this end, a general factorization theorem for bounded families in L∞(G) is proved from which we shall derive both results.

Next, we shall derive a contradiction as follows.

Nextly we shall derive the estimates of ρ and ξ.

In the following we shall derive the estimates of T i.

However, we shall derive one identity in detail and others can be obtained similarly.

We shall derive an open subset (K_{1} subset K) in which (5) is satisfied.

In this section, we shall derive the solvability for the problem ( P ) under certain conditions.