Scattering theory of partial differential equations and its applications

偏微分方程的散射理论及其应用

• 批准号: 06302010
• 负责人: IKAWA Mitsuru
• 金额: $ 3.26万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06302010/
• 关键词: partial differential equations; scattering theory; wave of earthquake; inverse problems; elastic equation; well posedness; nonlinear phenomenon; 散乱; シュレ-ディンガー作用素; 波動方程式; 散乱核; 極

Using this grand-in-aid, we organized seberal conferences of small size and of middle size. We studied the theory of partial differential equation, theoretically and concret problems in our daily life. The investigators shared the fields of problems and all the participants co-operated in integrating the researchs by organized by investigators.As we wrote in the above, we aimed to develope study of problems of partial differential equation in our daily life, and forcused the study to the inverse problems of partial differential equations, and developed the theoretial approach to these problems. Concerning the inverse problems, we experienced Kobe great earthquake during the period of our research. In fact, one of our main problem of research is a theoretical study of the inverse problem for the elastic wave, that is, the problem to determine the state of earth from the observation of the wave of earthquake. Even though Japan is a country of many earthquake, there are very few researcher in Mathematics. We have to develope the study of this inverse problems. Needless to say, we have to co-operate earth scientists, but we have to multiply the number of mathematicians interested in various problems related to earthquake.

利用这个巨大的援助，我们组织了小型和中型的会议。我们学习了偏微分方程的理论，从理论上和实际生活中的问题。研究者分享问题领域，所有参与者通过研究者的组织合作整合研究。正如我们在上面所写的，我们的目标是发展我们日常生活中的偏微分方程问题的研究，并将研究重点放在偏微分方程的反问题上，并发展这些问题的理论方法。关于反问题，我们在研究期间经历了科比大地震。实际上，我们研究的主要问题之一是弹性波反问题的理论研究，即从地震波的观测来确定地球状态的问题。虽然日本是一个多地震的国家，但很少有数学研究人员。我们必须开展对这一反问题的研究。不用说，我们必须与地球科学家合作，但我们必须增加对与地震有关的各种问题感兴趣的数学家的数量。

项目成果

A.Matsumura and M.Mei: "Nonlinear stability of viscous shock profile for a non-convex system of visco-elasticity" Comm.Math.Physics. (to appear).

A.Matsumura 和 M.Mei：“粘弹性非凸系统的粘性冲击曲线的非线性稳定性”Comm.Math.Physics。

T.Ichinose: "Some results on the relativistic Hamiltonian:Selfadjointness and imaginary-time path integral" Diff.Equation Math.Physics. 116-130 (1955)

T.Ichinose：“相对论哈密顿量的一些结果：自伴性和虚时间路径积分”微分方程数学物理。

T. Ichinose: "Some results on the relativistic Hamiltonian : Selfadjoint-ness and imaginary-time path integral" Differential Equations and Mathematical Physics. 116-130 (1995)

T. Ichinose：“相对论哈密顿量的一些结果：自共轭性和虚时间路径积分”微分方程和数学物理。

K. Mochizuki and R. Suzuki: "Critical exponent and ciritical bouw-up for quasilinear parabolic equatoins" Israel J. Math.(to appear).

K. Mochizuki 和 R. Suzuki：“拟线性抛物线方程的临界指数和临界曲线”Israel J. Math.（即将出现）。

K.Mochizuki: "Critical exponent and ciritical bouw-up for quasilinear parabolic equatoins" to appear in Israel J.Math.

K.Mochizuki：“拟线性抛物线方程的临界指数和临界曲线”出现在 Israel J.Math 中。