On the blow-up of sign-changing solutions to semilinear parabolic equations.

The article presents a study concerning the solution to the Cauchy problem for second-order semilinear parabolic equations which is the blow-up. According to the method being presented in the study the nonlinearity of the equation and solutions are not to be assumed as positive. It notes that Cauchy problem is analyzed through nonlinear method which is grounded on optimal test functions. It mentions that the study is backed up by the Program of the Russian Academy of Sciences "Modern Problems in Mathematics," and Russian Foundation for Basic Research.