Solvability of boundary value problems for fourth order systems of differential equations (Q1178082)

Let \(G\) be a bounded domain in \(\mathbb{R}^ n\) with piecewise smooth boundary and let \(Q=G\times(0,T)\), \(T>0\). The author considers the system \[ (K(X,t)u_ t)_ t-(A^{ij}(x,t)u_{x_ it})_{x_ jt}- (B^{ij}(x)u_{x_ it})x_ j \] \[ -(C^{ij}(x,t )u_{x_ i})_{x_ j}+A^ i(x)u_{x_ it}+A(x)u_ t+C(x,t)u=f(x,t) \] in domain \(Q\), where the coefficients \(A^{ij}\), \(B^{ij}\) and \(C^{ij}\) are elements of symmetric matrices, \(u\) and \(f\) are \(m\)-dimensional vector-valued functions, and the coefficients satisfy certain inequalities. He proves unique strong solvability of two boundary value problems for the system and for a system adjoint to it, in cases where \(f(x,t)\) belongs to spaces with a negative norm.