Academic Page of Dr. Isamu Ohnishi (Ph.D (Mathematical Science))
注意：勝手に ”おすすめページ” が表示されるようですが、私とは一切、関係ありません！ｗ
I'm Isamu Ohnishi (Ph.D (Mathematical Science)), whose main specialty (major) is
Mathematical Analysis of Nonlinear partial differential equations (N-PDE) with Dissipative structure. Namely, I am working to prove existence, uniqueness, and global well-posedness of solutions of N-PDE with dissipative structure mainly, and moreover, to prove characteristic behavior of the time global solution of it.
I have been obtaining main concerns not only to prove existence, uniqueness, global well-posedness of solutions of N-PDE with dissipative structure, but also to prove characteristic behavior of the time global solution of the N-PDE with dissipative structure. It is important that typical behaviors of the solution are classified from mathematically rigorous point of view.
Recently, I am concentrating to prove how solutions of a nonlinear parabolic partial differential equations with a certain kind of irregular gap term as a dissipative term. This is a very exciting work, I guess.
I will up here some of my recent papers (, preprints, and/or supplemental stuffs) of academic papers about my main works. Thank you very much for your visit here ! Please wait me a little with expectation to a new work of preprints. Stick around !!
Remark that, if you make DL to my preprints or something, then could you make a short comment in comment space for the corresponding article. Thank you in advance for your kindnesses.
with Best Regards,
Isamu Ohnishi. (Hiroshima University)
UNDER CONSTRUCTION !!!
In the near future, I will up my preprints here. Thank you in advance for your patience !
I. Academic works link (preprints):
(These are in preparation. Thank you for your patience. I 'm scheduling to be added sequentially.)
UNDER CONSTRUCTION !
II. Academic major works link (published already and only reviewed ) directly related to my main specialty:
In this chapter, I will up my main works from the viewpoint of the specialty. Only a part of the works have been upped here so far. I will be added the other works here sequentially.
UNDER CONSTRUCTION !!!!!
1. A mathematical study of the one dimensional Keller and Rubinow model for Liesegang bands, (J. Stat. Phys. 135, pages107–132 (2009))
2. ERRATUM: STABILITY OF STATIONARY SOLUTIONFOR THE LUGIATO-LEFEVER EQUATION, (Tohoku Math. J. 72, 487–492 (2020))
3. STABILITY OF A STATIONARY SOLUTION FOR THE LUGIATO-LEFEVER EQUATION, (Tohoku Math. J. 63 , 651–663 (2011))
4. Bifurcation analysis to the Lugiato–Lefever equation in one space dimension, (Physica D: Nonlinear Phenomena Volume 239, Issues 23–24, 1st. November 2010, Pages 2066-2083)
5. Inertial manifolds for Burgers' original model system of turbulence (Appl. Math. Lett. Vol. 7, No. 3, pp. 33-37, 1994 )
6. Some mathematical aspects of the micro-phase separation in diblock copolymers (Volume 84, Issues 1–2, 15 June 1995, Pages 31-39)
7. Mathematical analysis to coupled oscillators system with a conservation law
8. Analytical solutions describing the phase separation driven by a free energy functional containing a long-range interaction term
9. Standing pulse solutions for the FitzHugh-Nagumo equations
10. A Mathematical Aspects for Liesegang Phenomena
11. Spectral comparison between the second and the fourth order equations of conservative type with non-local terms
12.
UNDER CONSTRUCTION !!!
III. Academic minor works link (published already and only reviewed ) indirectly related to my main specialty:
In this chapter, I present some of my extra and minor works different from my main specialty. These are extra and minor, but these have gotten reviewed and published, as I have made them be quality reasonable.
Here, I will up my works indirectly related to my major work. These have been created by my pursuing my major works more excitingly. N-PDE with dissipative structure is very often a kind of model equations describing a certain phenomena essentially and mathematically in various scales of size. Once the model equation is created, then this should be analyzed in mathematical rigorous manner at least in the essential part, because, generally speaking, a mathematical model equation is independent from the original phenomena, once it is constructed. In spite of this fact, deep comprehension to the original phenomena must be still important, which tell us several suggestions very probably in mathematically rigorous analysis to the N-PDE with dissipative structure, and moreover, if the essential mechanism by which the phenomena can be done is understood mathematically rigorously, then we can tell something important for wider academic and/or social field from the viewpoint of mathematical science. It is said that abstraction is universalization by ancient sages, holy men.
I have investigated some another mathematical scientific or natural scientific fields' matters form the perspectives stated above. Of course, this is mainly because I would like to get an interesting N-PDE with dissipative structure as a model equation I would make a study, and sometimes this was ended successfully, and occasionally failed. In such activities, on the other hand, I sometimes got new (minor) results indirectly related to my main specialty. Those are my unexpected joys, and I have partially reported them for the time being. That is also partially because, if I didn't do it, then these were a kind of wasting time. Here you can see such kinds of works.
(1) Failure to the shortest path decision of an adaptive
transport network with double edges in Plasmodium
system
(2) Memory Reinforcement with Scale Effect and its Application to Mutual Symbiosis among Terrestrial Cyanobacteria of Nostochineae, Feather Mosses and Old Trees in Boreal Biome in Boreal Forests
(3) Standard model of a binary digit of memory with multiple covalent
modifications in a cell
(4) Dimension estimate of the global attractor for resonant motion of a spherical pendulum
(5) Dimension estimate of the global attractor for forced oscillation systems
(6) Fast Reaction Limits and Liesegang Bands
(7) A Mathematical analysis to Liesegang ring as a radially symmetric solution in n space dimensions
(8) Symmetry Breaking and Other Phenomena in the Optimization of Eigenvalues for Composite Membranes
(9) A billiard problem in nonlinear and nonequilibrium systems
(10) Mathematical analysis to an adaptive network of the Plasmodium system
(11) Macroscopic pattern formation of liquid crystal in kappa carrageenan gel
(12) Physarum can solve the shortest path problem on Riemannian surface mathematically rigorously
(13)
UNDER CONSTRUCTION !!!
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