THE COMPOUND BOUNDARY VALUE PROBLEM FOR A CLASS OF NONLINEAR PSEUDOPARABOLIC SYSTEMS

Let D be N+1 connected bounded domain in plane. Suppose the contour of D consists of N+1 simple-ly closed curves _0, _1…, _N and _1… _N are in the interior of domain circumscribed byC_μ~1(0 <μ< 1). In addition, assume that there are n mutually exclusive contour γ_,j=1,…,n,in interi-or of D,γ=γ_i; ∈C_μ~1. Denote D_j is the bounded domain circumscribed by γ_j,j=1,…,n, D~-=D_1+…+D.,D~+=D-D~-,D_t~ =D~ ×E, E=[0,T] (T>0), z=0∈D~+.We consider the following pseudoparabolic complex equation on D_t~ : / t[W_Z- Q_1(z)W_z- Q_2(z) _ - A_1(z)W - A_2(Z) ]= H(t,z,W,W-_2,W_2), (z,t) ∈D_t~ , (1)