拟线性抛物型方程边值问题时间周期解-重庆师范大学学报（自然科学版）

文章信息/Info

Title:: Time Periodic Solutions to Boundary Value Problem of Quasi-linear Parabolic Equations

Author(s):: ZHA Zhong-wei; College of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing Wanzhou 404000, China

Keywords:: quasilinear parabolic equation; boundary value problem; Hö; lder continuous function; T-periodic solution

摘要:: 研究一类拟线性抛物型方程的边值问题， Ω ={(x, t) | 0 < x < l, - ∞ < t < + ∞} 。首先引入时间周期的 Hölder 连续函数空间 (Ω), 和函数 F (x, t, w)= ，在已知函数的某些假设条件下，利用上下解方法和 Leray-Schauder 不动点定理证明了边值问题有满足 j (x)≤u(x, t)≤j(x) 的时间周期解 u (x, t)∈ (Ω) 。由函数 F 的定义推断出所研究的边值问题时间周期解的存在性。

Abstract:: The boundary value problem of a kind of quasi-linear parabolic equations is discussed. , Ω={(x, t) | 0 < x < l, - ∞ < t < + ∞}.This paper firstly introduces H ö lder space (Ω) of T-periodic continuous function and following function: F(x, t, w)= . The time periodic solution u(x, t) which satisfied j(x)≤u(x, t)≤j(x)is obtained under some assumed conditions of known functions, by use of method upper and lower solution and Leray –Schauder fixed-point theorem to following boundary value problem . The existence of time periodic solution to boundary value problem is proved by the definition of the function F.