On nonlocal problems for pseudoparabolic equations (Q1114861)

Three nonlocal problems for pseudoparabolic equations are considered. The method of solving these problems is based on constructing the Riemann function for the differential operator of third order \[ Lu\equiv u_{xxt}+Au_{xx}+a(x)u_ x+b(x,t)u_ t+c(x)u, \] \[ (x,t)\in \Omega;\quad \Omega =\{(x,t):\quad x\in (0,1),\quad t\in (0,T),\quad 0<1,T<\infty \}, \] A\(=const.\), \(a\in C^ 1[0,1]\), \(c\in C^ 1[0,1]\), \(b\in C^ 1(\Omega)\), \(b(x,t)<0\). The problems lead to respective integral equations. Sufficient conditions for the existence of solutions are given.