In the real Sobolev space H1
0 (Ω) we consider the Cauchy-Dirichlet problem for sine-Gordon type
equation with strongly elliptic operators and two small parameters. Using some a priori estimates of solutions
to the perturbed problem and a relationship between solutions in the linear case, we establish convergence estimates for the difference of solutions to the perturbed and corresponding unperturbed problems. We obtain that
the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood
of t = 0
