Study for spectrum of dissipative operators and classification for the solutions of dissipative equations

耗散算子谱的研究及耗散方程解的分类

基本信息

  • 批准号:
    16540161
  • 负责人:
  • 金额:
    $ 1.98万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    2004
  • 资助国家:
    日本
  • 起止时间:
    2004 至 2006
  • 项目状态:
    已结题

项目摘要

1. One dimensional Scheodinger and wave equations with dissipative perturbation of rank oneBy using scattering theory, we deal with Scheodinger equations with delta function as dissipative perturbation and wave equations with some dissipative term. Our assumptions of perturbation are special or artificial. However, to characterize the spectrum of generator (dissipative operator ) of equation these assumptions are need. Using the spectrum of generator obtained we construct Parseval formula and classify the behavior of the solutions. Concretely, initial data associated with real continuous spectrum and non-real spectrum are evolved scattering state and dissipative state, respectively. Therefore any solutions are represented as linear combination of these states2. Spectral structure of generator of wave equations with some dissipations and exponential decay solutionsFor wave equations with Coulomb type dissipative term or dissipative boundary condition at origin dissipations, we show existence of exponential decay or disappearing solutions. Especially we show that the spectrum of generator associated with wave equations with Coulomb type dissipative term consists with complex lower half-plain. However we do not characterize the relation between the spectrum and exponential or disappearing solution.3. Eigenfunction expansion of solutions for wave equations with dissipative boundary condition on finite intervalWe show that any solutions are represented by using eigenfunction for the generator of wave equations. The proof is done by using the separation of variable and usual Fourier series. However the solutions are represented in the energy space not usual LA 2-space4. Out-going and In-coming subspaces of Lax-Phillips type and the proof for asymptotic completeness of wave operatorsWe give new definition of Out-going and In-coming spaces by using the idea of Lax-Phillips(1967). Using these subspaces and combining the proof of Perry(1980) we show asymptotic completeness.
1。使用散射理论对等级Oneby的耗散扰动的一维Scheodinger和波动方程,我们将具有Delta函数的Scheodinger方程作为耗散性扰动和波浪方程,并具有一定的耗散项。我们对扰动的假设是特殊或人为的。但是,为了表征方程的发生器(耗散算子)的频谱,这些假设是需要的。使用获得的生成器的光谱,我们构建parseval公式并对溶液的行为进行分类。具体而言,与实际连续频谱和非现实光谱相关的初始数据分别是进化的散射状态和耗散状态。因此,任何解决方案表示为这些状态的线性组合2。波动方程的生成器的光谱结构具有一些耗散和指数衰减的溶液,用于具有库仑型耗散项或原点耗散的耗散边界条件的波浪方程,我们显示了指数衰减或消失的溶液的存在。尤其是我们表明,与库仑类型耗散术语的波动方程相关的发电机频谱与复杂的下半平台组成。但是,我们没有表征频谱与指数或消失解决方案之间的关系。3。有限间隔上具有耗散边界条件的波方程的溶液的本征函数扩展表明,通过使用特征功能对波方程的发电机使用特征功能来表示任何溶液。该证明是通过使用变量和通常的傅立叶系列的分离来完成的。但是,这些解决方案在能量空间中代表,而不是通常的LA 2空间4。 Lax-Phillips类型的外向和内部子空间以及Wave Operators的渐近完整性的证明,我们通过使用Lax-Phillips的想法(1967)为外向和室内空间提供了新的定义。使用这些子空间并结合了Perry(1980)的证明,我们显示了渐近完整性。

项目成果

期刊论文数量(74)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A note on the nonrelativistic limit of Dirac operators and spectral concentration
关于狄拉克算子的非相对论极限和谱浓度的注解
Total energy decay for the wave equation in exterior domain With a dissipation near infity
耗散接近无穷大的波动方程在外域的总能量衰减
  • DOI:
  • 发表时间:
    2007
  • 期刊:
  • 影响因子:
    0
  • 作者:
    K.Mochizuki;M.Nakao
  • 通讯作者:
    M.Nakao
Inverse scattering problem in nuclear physics- optical model
核物理-光学模型中的逆散射问题
Interface vanishing for solutions to Maxwell and Stokes systems
麦克斯韦和斯托克斯系统解决方案的界面消失
Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy
具有空间各向异性耗散项的波动方程总能量不衰减
  • DOI:
  • 发表时间:
    2004
  • 期刊:
  • 影响因子:
    0
  • 作者:
    川下美潮;川下和日子;曽我日出夫
  • 通讯作者:
    曽我日出夫
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KADOWAKI Mitsuteru其他文献

KADOWAKI Mitsuteru的其他文献

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{{ truncateString('KADOWAKI Mitsuteru', 18)}}的其他基金

Research on the asymptotic form of the solutions to the Helmholtz equation and the application to mathematical scattering theory
亥姆霍兹方程解的渐近形式及其在数学散射理论中的应用研究
  • 批准号:
    22540198
  • 财政年份:
    2010
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Research on spectral structure of dissipative operators and super composition of dissipative systems
耗散算子谱结构及耗散系统超组合研究
  • 批准号:
    19540189
  • 财政年份:
    2007
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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