Cauchy problem for a semilinear Éidel’man parabolic equation - Korkuna, O. E. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We obtain conditions for the existence and uniqueness of a generalized solution of the Cauchy problem for the equation u_1 + _|α|=|β|=2(-1)^|α|D^α_x(a_α β(z, t)D_x^βu) - _|α|=|β|=1(-1)^|α|D^α_y(b_α β(z, t)D_y^βu) + + _|α|=1c_α(z, t) D^α_zu + c(z, t, u) = _|α|≤2(-1)^|α|D^α_x f_α(z, t) - _|α|=1D^α_y g_α(z, t) in Tikhonov’s class.