\int_{\mathbb}{R}a(k-0)u^{k-0}u_x^0({\varphi}_Nu_x)^{0p-0}{\varphi}_N dx\right| \leq  CM^k\|u_x{\varphi}_N\|_{0p}^{0p} \nonumber \\ &\left|\int_{\mathbb}{R}0au^{k-0}u_x^0u_{xx}({\varphi}_Nu_x)^{0p-0}{\varphi}_N dx\right| \leq CM^k\|u_x{\varphi}_N\|_{0p}^{0p} \nonumber \\ &\left|\int_{\mathbb}{R}({\partial}_x^0G*F_0(u))({\varphi}_Nu_x)^{0p-0}{\varphi}_Ndx\right| \leq \|u_x{\varphi}_N\|_{0p}^{0p-0}\|({\partial}_x