The Problem Of Even Order And Partial Differential Equation Of Mixed Type

This article studies the mixed problem for a class of even-order partial differentialequations, and change in the boundary problem of a class of even partial differentialequations, a class of mixed hyperbolic-parabolic equation changes in border issues.The hybrid equation is the special research directions of partial differential equations,and is a promotion of partial differential equations.Domestic and foreign scholars hada lot of fruitful work in this area. About mixed problem.Many scholars in Russia havedone a lot of research on the development of even-order partial differential equations,and many more perfect conclusions.Involving nonlinear and changes in border issues,is an important and interesting problems. This article is divided into five sectionsdescribed these problems.The first part, is about the even-order partial differential equations and theequation of mixed background, significance and it’s research.The second part, describes the preparation the knowledge used in this article.The third part gives a kind of even order partial differential equations aboutmixed problems, changes in the boundary problem of a class of even partialdifferential equations, a class of mixed hyperbolic-parabolic equation changes inborder issues.SectionⅠis about description of the problem and the underlying assumption.In sectionⅡ,studies priori estimates of solution,and get theorem3.2.1.In sectionⅢ,studies the uniqueness of solution,and get theorem3.3.1.In sectionⅣ,studies the existence of solution which we first get the solution thatform of infinite series,and then prove the existence theorem of solution. Then use thefixed point theorem and infinite series absolutely convergent criterion, to prove theexistence of solution. And get the theorem3.4.1and theorem3.4.2which given in thearticle.PartⅣ discusses the changes in the boundary problem of a class of even-orderpartial differential equations.In sectionⅠ,put forward the questions. In sectionⅡ,study priori estimates of solution and get the theorem4.3.1.PartⅤunknown boundary problem about a class of mixed hyperbolic-parabolicequation.In sectionⅠ,put forward the questions.In sectionⅡ,discusses the priori estimates of unknown boundary problem about aclass of mixed hyperbolic-parabolic equation, get the theorem5.2.1and theorem5.2.2.In sectionⅢ,studies the uniqueness of solution on unknown boundary problemabout a class of mixed hyperbolic-parabolic equation, get the theorem5.3.1.