For this system of equations the questions of existence, regularity and the stability of solution are analysed.
Another cluster of experiences dealt with the regularity or existence of follow-up consultations.
Based on the maximal Sobolev regularity, the existence of a unique global bounded classical solution of the problem is established under the assumption that both (mu_{1}) and (mu_{2}) are sufficiently large.
In [15], Felmer et al. considered the regularity and existence of solutions under the famous Ambrosetti Rabinowitz (A R) condition, i.e., there exists (theta> 2) such that (0 < theta F x,t) < tf x,t)).
Later on, Qin et al. [8, 9] proved the regularity of weak solutions and existence of classical solution.
The closedness of each T ( x ) and the regularity of X imply the existence of a real number r 2 > 0 such that B ( x 0, r 2 ) ∩ T ( x ) = ∅ for each x ∈ B ( x 0, r 1 ), which implies x 0 ∉ B ( T ( x ) ; r 2 ) for each x ∈ B ( x 0, r 1 ).
The closedness of each T ( ω, z ) and the regularity of X imply the existence of a real number r 2 > 0 such that B ( ξ 0 , r 2 ) ∩ T ( ω, z ) = ∅ for each z ∈ B ( ξ 0 , r 1 ), which implies ξ 0 ∉ B ( T ( ω, z ) ; r 2 ) for each z ∈ B ( ξ 0 , r 1 ).
We discuss possible origins of this regularity and the existence of a universal mechanism deciding the length of the user posts.
We obtain results of existence, uniqueness, maximal regularity and optimal dependence on the parameter δ for Lp solutions of the problem.
They established the existence and uniqueness of local and global mild solutions and proved the existence and regularity of classical solutions.
