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$$u_t + f(u)_x = g(t,x) \hspace*{2em}(u=u(t,x)\in\mbox{\sl R},\hspace*{1em}f''(u)>0)$$ (1)

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$$f''(u)\geq\delta \hspace*{2em}(u\in\mbox{\sl R})$$ (2)

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$$\int_0^T dt \int_0^1 g(t,x)dx = 0$$ (3)

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$$\tilde{g}(t,x)-\tilde{g}(t,y)\leq G_1(x-y) \hspace*{2em}(x>y)$$ (4)

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$$u(t,0)=u(t,1) \hspace*{2em}(0<t<T)$$ (5)

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$$u(T,x)=u(0,x),\hspace*{2em}\int_0^1 u(0,x)=\bar{u}$$

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