EXAMPLE OF DIMENSION REDUCTION IN ONE-DIMENSIONAL EVOLUTIONARY PROBLEMS
Simplifications of the first-order PDE systems with the help of dimension reduction in overdetermined systems of partial differential equations are considered. A new method for overriding any system of partial differential equations is proposed. This overdetermination is investigated using the example of one-dimensional evolution equations. Analytic examples are given where by this method the Cauchy problem for two-dimensional systems of equations can be reduced to the parametric Cauchy problem for an ODE, whose solution is then found explicitly.