Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an e...Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.展开更多
We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,u<sub>x</sub>,u<sub>xx</sub>)+b（x,t,u,u<sub>x</sub>）,（x,t）∈（-1,1）×...We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,u<sub>x</sub>,u<sub>xx</sub>)+b（x,t,u,u<sub>x</sub>）,（x,t）∈（-1,1）×(0,T], u（±1,t）=0,u（x,0）=■（x）, where a is strongly nonlinear with respect to u<sub>xx</sub>and ■ is not necessarily small.We also deal with nonuniform case.展开更多
文摘Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.
基金Supported by the Open Office of Mathematica Institute,Academia Sinica.
文摘We discuss the existence of global classical solution for the uniformly parabolic equation ■ut=a(x,t,u,u<sub>x</sub>,u<sub>xx</sub>)+b（x,t,u,u<sub>x</sub>）,（x,t）∈（-1,1）×(0,T], u（±1,t）=0,u（x,0）=■（x）, where a is strongly nonlinear with respect to u<sub>xx</sub>and ■ is not necessarily small.We also deal with nonuniform case.
