On a certain limit problem for some class of parabolic differential equations of the fourth order (Q1092232)

The aim of the paper is a boundary value problem for the equation \(P_ 1P_ 2u(x,t)=f(x,t)\), \(P_ i=D^ 2_ x-C_ iD_ t\) in the strip \(D=\{(x,t):| x| <a\), \(t\in (0,T)\), \(T<\infty \}\), where \(a,C_ i,i=1,2\) are positive constants. The initial conditions are of the form \(P^ i_ 2u(x,0)=f_ i(x)\), \(i=0,1\), the boundary conditions are of the form \(P^ i_ 2u(-a,t)=h_ i(t)\), \(P^ i_ 2u(a,t)=h_ i(t)\), \(i=0,1\). In order to solve this problem suitable Green's functions \(g_ 1,g_ 2\) are used. Existence and uniqueness theorems are given.