高階Schrodinger方程的時(shí)空估計(jì).pdf

1、華中科技大學(xué)碩士學(xué)位論文高階Schrodinger方程的時(shí)空估計(jì)姓名：鄧超申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：鄭權(quán)20080428華 中 科 技 大 學(xué) 碩 士 學(xué) 位 論 文AbstractHarmonic analysis which originated from the work of some famous mathematicianssuch as Euler and Fourier has developed int

2、o one of the most interesting subjects of modernmathematics in the following 200 years. These powerful methods have a wider range ofapplications in many other subjects of mathematics and are especially successful for par

3、tialdifferential equations.The applications in partial differential equations can be presented in the following twoaspects: The fi rst one is its application to elliptic partial differential equation problems withboundar

4、y value. In Lip border region, Stein together with his partners achieved the Lpestimates and regularities of the solution of second order elliptic equations with boundaryvalue.And another aspect is that harmonic analysis

5、 plays an important role in the researchof evolution equations.The Lp ? Lq estimates and the corresponding time-space estimates of the linear equa-tions provide us with new research tools in dealing with nonlinear equati

6、on problem. Forexample: with time-space estimates and some nonlinear estimates,we can establish manyuseful estimates of nonlinear Schr¨ odinger equation.This thesis will be organized as follows.In the fi rst chapter

7、,the author will give someintroduction of time-space estimates.Then in the following chapter,the author provedthe time-space estimate of higher order Schr¨ odinger equation on Besov spcae.In the lastchapter,the auth

8、er gives some application of the locally smoothing effects of higher orderSchr¨ odinger equations.Key words:Besov space time-space estimate Schr¨ odinger equation Car-leson conjecture phase function oscillatory