The uniqueness class for the Cauchy problem for pseudoparabolic equations Academic Article

It is shown that the class of functions satisfying | u ( x , t ) | M e | x | |u(x,t)| leqslant M{e^{alpha |x|}} forms a uniqueness class for the Cauchy problem for pseudoparabolic equations. The surprising fact is that, unlike the case of parabolic equations, the constant alpha is not arbitrary but depends on the coefficients of the equation.