We suggest a scenario of spontaneous (or dynamical) C and CP violation according to which it is possible to generate domains of matter and antimatter separated by cosmologically large distances. Such C(CP) violation existed only in the early universe and later it disappeared with the only trace of generated matter and antimatter domains. So this scenario does not suffer from the problem of domain walls. According to this scenario the width of the domain wall should grow exponentially to prevent annihilation at the domain boundaries. Though there is a classical result obtained by Basu and Vilenkin that the width of the wall tends to the one of the stationary solution (constant physical width). That is why we considered thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we were interested not only in stationary solutions found therein, but also investigated the general case of domain wall evolution with time. When the wall thickness parameter, δ0, is smaller than where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for An explanation for the critical value is also proposed.