耗散模型中的非线性问题
Non linear problems in dissipative models
摘要：
对一类拟线性抛物型三阶方程进行定性分析，该方程描述了一类耗散模型的演化。作为一些典型的边界问题的例子，Dirichlet和Neumann的类型的边界条件进行检查。在线性的情况下，相关的格林函数明确确定，连同严格的估计，他们的行为时，参数的耗散是零。这些结果是研究积分方程的基础，从而使非线性问题转化为积分方程。此外，也可以确定边界层估计。
英文摘要：
Aim of the paper is the qualitative analysis of a quasi-linear parabolic third order equation, which describes the evolution in a large class of dissipative models. As examples of some typical boundary problems, both Dirichlet's and Neumann's type boundary conditions are examined. In the linear case, the related Green functions are explicitly determined, together with rigorous estimates of their behavior when the parameter of dissipation is vanishing. These results are basic to study the integral equations to which the non linear problems can be reduced. Moreover, boundary layer estimates can be determined too.
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