An inverse problem for a 2D parabolic equation with nonlocal overdetermination condition - Kinash, N.Ye. (Carpathian Mathematical Publications, 2016)
We consider an inverse problem of identifying the time-dependent coefficient a(t) in a two-dimensional parabolic equation: u_t=a(t)Δ u+b_1(x,y,t)u_x+b_2(x,y,t)u_y+c(x,y,t)u+f(x,y,t), (x,y,t)Q_T, with the initial condition, Neumann boundary data and the nonlocal overdetermination condition u_1(t)u(0,y_0,t)+ u_2(t)u(h,y_0,t)=μ_3(t),t[0,T], where y_0 is a fixed number from [0,l]. The conditions of existence and uniqueness of the classical solution to this problem are established. For this purpose the Green function method, Schauder fixed point theorem and the theory of Volterra intergral equations are utilized.