Mishio Kawashita

Last Updated :2021/04/26

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Professor
E-mail
kawasitahiroshima-u.ac.jp
Self-introduction
In mathematical analysis, I study focusing on the initial boundary value problem of such partial differential equations as a wave equation and a heat equation. First, I am conducting mathematical analysis of a wave propagation phenomenon or a stationary state. I expect applying the result to the related problem including inverse problems formulated by the differential equation and analysis of phenomena of energy propagation.

Basic Information

Major Professional Backgrounds

  • 1989/04/01, 1993/03/31, Kochi University, Faculty of Science, Research Associate
  • 1993/04/01, 2001/09/30, Ibaraki University, Faculty of Education, Associate Professor
  • 2001/10/01, 2007/03/31, Hiroshima University, Graduate School of Science, Associate Professor
  • 2007/04/01, 2012/03/31, Hiroshima University, Graduate School of Science, Associate Professor
  • 2012/04/01, 2020/03/31, Hiroshima University, Graduate School of Science, Professor

Educational Backgrounds

  • Osaka University, Graduate School, Division of Natural Science, Department of Mathematics, Japan, 1988/04, 1989/03
  • Osaka University, Faculty of Science, Department of Mathematics, Japan, 1982/04, 1986/03

Academic Degrees

  • Doctor of Science, Osaka University
  • Master of Science, Osaka University

Educational Activity

  • 【Bachelor Degree Program】School of Science : Mathematics
  • 【Master's Program】Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program
  • 【Doctoral Program】Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Educational Activity

Course in Charge

  1. 2021, Liberal Arts Education Program1, 1Term, Seminar in Linear AlgebraI
  2. 2021, Liberal Arts Education Program1, 2Term, CalculusI
  3. 2021, Undergraduate Education, 4Term, Analysis IV
  4. 2021, Undergraduate Education, 4Term, Exercises in Analysis IV
  5. 2021, Undergraduate Education, 1Term, Exercises in Analysis B
  6. 2021, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  7. 2021, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  8. 2021, Graduate Education (Master's Program) , First Semester, Seminar in Mathematics
  9. 2021, Graduate Education (Master's Program) , Second Semester, Seminar in Mathematics
  10. 2021, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics
  11. 2021, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics
  12. 2021, Graduate Education (Master's Program) , First Semester, Seminar of Real Analysis and Functional Equation
  13. 2021, Graduate Education (Master's Program) , Second Semester, Seminar of Real Analysis and Functional Equation
  14. 2021, Graduate Education (Master's Program) , 4Term, Mathematical Analysis B
  15. 2021, Graduate Education (Master's Program) , 3Term, Topics in Mathematical Analysis A
  16. 2021, Graduate Education (Master's Program) , 4Term, Topics in Mathematical Analysis B
  17. 2021, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
  18. 2021, Graduate Education (Master's Program) , Academic Year, Seminar on Real Analysis and Functional Equations
  19. 2021, Graduate Education (Master's Program) , Academic Year, Seminar on Real Analysis and Functional Equations
  20. 2021, Graduate Education (Master's Program) , 1Term, Mathematical Analysis A
  21. 2021, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  22. 2021, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  23. 2021, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  24. 2021, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  25. 2021, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. Mode-conversion of the scattering kernel for the elastic wave equation, Journal of the Mathematical Society of Japan, 42(4), 691-712, 19900401
  2. On the local-energy decay property for the elastic wave equation with the Neumann boundary condition, Duke Math. J., 67(2), 333-351, 19920401
  3. On the decay rate of local energy for the elastic wave equation, Osaka Journal of Mathematics, 30(4), 813-837, 19930401
  4. On the region free from the poles of the resolvent for the elastic wave equation with the Neumann boundary condition, Japan Academy. Proceedings. Series A. Mathematical Sciences, 69(10), 339-402, 19930401
  5. Another proof of the representation formula of the scattering kernel for the elastic wave equation, Tsukuba Journal of Mathematics, 18(2), 351-369, 19940401
  6. On a region free from the poles of the resolvent and decay rate of the local energy for the elastic wave equation, Indiana University Mathematics Journal, 43(3), 1013-1043, 19940401
  7. The poles of the resolvent for the exterior Neumann problem of anisotropic elasticity, SIAM Journal on Mathematical Analysis, 31(4), 701-725, 20000401
  8. Harmonic moments and an Inverse problem for the heat equation, SIAM Journal on Mathematical Analysis, 32(3), 522-537, 20000401
  9. Properties of elastic symbols and construction of solutions of the Dirichlet problem, Korean Mathematical Society. Communications, 16(3), 399-404, 20010401
  10. Eshelby tensor of a polygonal inclusion and its special properties, J. Elasticity, 64(1), 71-84, 20010401
  11. On global solutions of Cauchy problems for compressible Navier-Stokes equations, Nonlinear Analysis= Theory= Methods ans Applications, 48, 1087-1105, 20020101
  12. Complex analysis of elastic symbols and construction of plane wave solutions in the half-space, J. of Math. Soc. Japan, 55, 395-404, 20030401
  13. Energy behaviour of the Rayleigh waves in 3-dimensional half space, Math. Proc. Cambridge Philos. Soc., 135, 545-563, 20030401
  14. Relation between scattering theories of the Wilcox and Lax-Phillips types and a concrete construction of the translation representation, Comm. Partial Differential Equations, 28(8), 1437-1470, 20030401
  15. Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy, Nagoya J. Math., 174, 115-126, 20040401
  16. Analyticity of the Resolvent for Elastic Waves in a Perturbed Isotropic Half Space, Math. Nachr., 278(10), 1163-1179, 20050401
  17. Scattering theory for the elastic wave equation in perturbed half-spaces, Trans. Amer. Math. Soc., 358(12), 5319-5350, 20061210
  18. The enclosure method for the heat equation, INVERSE PROBLEMS, 25(7), 200907
  19. Singular Support of the Scattering Kernel for the Rayleigh Wave in Perturbed Half-Spaces., Methods and Applications of Analysis, 17(1), 1-48, 2010
  20. On the reconstruction of inclusions in a heat conductive body from dynamical boundary data over a finite time interval, INVERSE PROBLEMS, 26(9), 201009
  21. Weighted energy estimates for wave equations in exterior domains, FORUM MATHEMATICUM, 23(6), 1217-1258, 201111
  22. Local energy decay for wave equations in exterior domains with regular or fast decaying dissipations, SUT Journal of Mathematics, 47(2), 143-159, 2011
  23. Estimates of the integral kernels arising from inverse problems for a three-dimensional heat equation in thermal imaging, KYOTO JOURNAL OF MATHEMATICS, 54(1), 1-50, 2014
  24. AN INVERSE PROBLEM FOR A THREE-DIMENSIONAL HEAT EQUATION IN THERMAL IMAGING AND THA ENCLOSURE METHOD, INVERSE PROBLEMS AND IMAGING, 8(4), 1073-1116, 201411
  25. A moment method on inverse problems for the heat equation, the proceeding of the Japan and Korea joint scientific seminar on Inverse problems and related topics (Kobe 1988), G. Nakamura et. al. (ed.), 81-88, 2000
  26. Scattering of elastic waves in the half-space and relation between the Lax-Phillips theory and the Wilcox theory, Recent development in theories and numerics, International conference on inverse problems, Y.C. Hon et. al. (ed.), 182-191, 2003
  27. Sufficient conditions for decay estimates of the local energy and a behavior of the total energy of dissipative wave equations in exterior domains, HOKKAIDO MATHEMATICAL JOURNAL, 46(3), 277-313, 2017
  28. ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR THE LAPLACE EQUATION WITH A LARGE SPECTRAL PARAMETER AND THE INHOMOGENEOUS ROBIN TYPE CONDITIONS, OSAKA JOURNAL OF MATHEMATICS, 55(1), 117-163, 201801
  29. ON FINDING A BURIED OBSTACLE IN A LAYERED MEDIUM VIA THE TIME DOMAIN ENCLOSURE METHOD, INVERSE PROBLEMS AND IMAGING, 12(5), 1173-1198, 201810
  30. ON FINDING A BURIED OBSTACLE IN A LAYERED MEDIUM VIA THE TIME DOMAIN ENCLOSURE METHOD IN THE CASE OF POSSIBLE TOTAL REFLECTION PHENOMENA, INVERSE PROBLEMS AND IMAGING, 13(5), 959-981, 201910

Invited Lecture, Oral Presentation, Poster Presentation

  1. Decaying properties of the total and local energies for the wave equations with dissipations, Mishio Kawashita, The 7 th Pacific RIM Conference on Mathematics 2016, 2016/06/28, With Invitation, English, Room 406, Department of Mathematical Sciences, Seoul National University, Korea
  2. Decaying properties of the total and local energies for the wave equations with dissipations, Mishio Kawashita, Séminaire d'analyse, 2016/10/07, Without Invitation, English, Des Mathématiques à Nantes, Université de Nantes
  3. Asymptotics of the function corresponding to refracted waves for the flat transmission boundary and the enclosure method, Mishio Kawashita, Masaru Ikehata, RIMS Workshop on "Inverse problems for partial differential equations and related areas", 2017/01/26, With Invitation, English, RIMS Kyoto University, RIMS Kyoto University
  4. Finding obstacles in a two-layered medium by the enclosure method, Mishio Kawashita, Inverse Problems for Partial Differential Equations In honor of Professor Masaru Ikehata on the occasion of his 60th Birthday, 2018/08/26, With Invitation, English
  5. The enclosure method for the time dependent problems and the shortest lengths, Mishio Kawashita, International Workshop on Inverse Problems for Partial Differential Equations, 2018/09/10, With Invitation, English, School of Mathematics, Southeast University, China, School of Mathematics, Southeast University, China

Social Activities

Organizing Academic Conferences, etc.

  1. Regularity and Singularity for Partial Differential Equations with Conservation Laws, Organizer(chief), 2013/06, 2013/06
  2. Regularity and Singularity for Partial Differential Equations with Conservation Laws, Organizer(chief), 2014/05, 2014/05
  3. International Conference on Recent Advances in Hyperbolic Partial Differential Equations, Organizer, 2014/12, 2014/12
  4. Regularity and Singularity for Partial Differential Equations with Conservation Laws, Organizer(chief), 2015/06, 2015/06
  5. Inverse Problems for Partial Differential Equations In honor of Professor Masaru Ikehata on the occasion of his 60th Birthday, organizer(Chief), 2018/08, 2018/08