INVESTIGATION OF UNIQUENESS OF ALMOST EVERYWHERE SOLUTION OF ONE-DIMENSIONAL MIXED PROBLEM FOR A KORTEWEG-DE FRIES-BURGERS TYPE NON-LINEAR EQUATION

The problem studies a problem on uniqueness of almost everywhere solution of one-dimensional mixed problem with Rikier type conditions for a class of semi-linear pseudoparabolic differential equations of the fifth order of Kortewegde Fries-Burgers type. Almost everywhere solution of the considered mixed problem is sought in the form of Fourier series u(t, x) = Sigma(infinity)(n=1) u(n) (t) sin nx and after application of the Fourier method the finding of Fourier unknown coefficients u(n)( t) (n = 1, 2, ...) of the desired solution is reduced to the solution of some of countable system of Volterra type nonlinear integral equations. Furter, by means of the Bellman inequality a theorem on global uniqueness of almost everywhere solution of the studied mixed problem is proved.