This paper considers the strong convergence of the Lρoc(R+ ×R) (1<p <+ ∞) uniformly bounded approximate solutions to the Cauchy problem of the following scalar conservation laws A new compactness result is obtained, in which f(u) isn t asked to satisfy any growth condition at infinity.

By combining the Newton method with the method of harmonic balance(HB),we have established improved analytical approximations to the period and the corresponding periodic solution to the non-linear Jerk equations.

Based on the analytical approximations to period of nonlinear oscillators with even potential functions,a new analytical approximate period to nonlinear oscillators with general potential functions is established.

The new analytical approximations for the buckling load and the largest deflection of the Euler\'s column show an excellent agreement with the numerically exact ones,and are valid over nearly the whole range of the independent variable.