| In this paper we study the initial boundary value problem of the mixed type equation, which is one of the special study directions in partial differential equation .Much fruitful research work have been made by many scholars at home and abroad on this respect .The problem on changing boundary and non-local peoblem is an important and interesting issue. This paper is divided into five parts to discuss these issues.In part1, we describes the research background,the present research situation and the research meaning of the mixed type equation.In part2, we introduce the preliminary knowledge concerning the article.In part3, we state the dimensional mixed hyperbolic– parabolic of Cauchy problems.In Section 1, we state of the problem.In Section2, we discussed the prior model solution for the problem and the solution estimates, uniqueness and stability, by Theorem 3.2.1 of this paper, Theorem 3.2.2, Theorem 3.2.3, Theorem 3.2.4, Theorem 3.2. 5, Theorem 3.2.6.In Section3, we gives the existence and uniqueness, in the use of the convergence theorem of series solution for the problem have proved the existence of the text in the Theorem by 3.3.1, Theorem 3.3.2.In part4,we discussed a class of mixed-type equation by the boundary problem.In Section 1,we first of all ask questions.In Section2,we state the problem in the region on the solution uniqueness. Has been the text in the Theorem 4.2.1, Theorem 4.2.1.In part5, this is an important part of this article, the main research is mixed parabolic - semi-parabolic equation by the boundary problem.In Section 1, we ask questions.In Section 2,we discusses the problem in different regions of the uniqueness of the solution was to get the text in the Theorem 5.1.1, Theorem 5.1.2.In Section 3, we according to Green formula, the problem of integral solutions obtained, reasonable use of the fixed point theorem, was proved the existence of Solutions. Get the text in the Theorem 5.2.1, Theorem 5.2.2. |
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