摘要
讨论了一类半线性抛物型方程组问题，其非线性项具有拟单调性，边界条件是耦合非局部型的．文中考虑的问题的边界条件中耦合积分核是变号的，为此引入新的上解和下解的定义，在一定条件下，建立了上解和下解的有序性．通过单调迭代等方法得到问题解的存在性和唯一性。
It aims at the investigation of a system of nonlinear
partial differential equations of parabolic type which is motivated by the model problems arising
from quasi state hygrothermoelasticity, pathology and population dynamics etc.. The nonlinear
terms of the problem are quasi monotonic, and the boundary value conditions are coupled and
nonlocal. Since the coupled integration kernels in the boundary value conditions possess
alternating sign in their domain, a new definition of upper and lower solutions was introduced.
Under some hypotheses, the upper and lower solutions can be ordered. The existence and
uniqueness of solutions to the problem were obtained by using monotonic iteration method. An
example gave an illustration of results here. The results extend the study for the nonlocal
boundary value problems of partial differential equations.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
1999年第6期676-679,共4页
Journal of Shanghai Jiaotong University
关键词
非局部问题
抛物型方程组
边值问题
解
存在性
nonlocal problem
parabolic partial differential equations
boundary value problems
existence
