>>List by Field@>>Research Fellowship for Young Scientists @>>Professor Emeritus
Ogawa Takayoshi , Professor 
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Research field



Real Analysis, Functional Analysis and
Applied Analysis based on Partial Differential
Equations.


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Research 


@ I have been analytically examining various types of partial differential equations that appear in mathematical physics (which often take the form of nonlinear equations) with respect to real analysis (expanded version of the Lebesque integral theory or Fourier analysis), and functional analysis (linear algebra of infinite dimensions). Especially, I am interested in the socalled gcriticalh problem in which the linear structure and the nonlinear structure are balanced. Strangely enough, this gcritical situationh often appears in mathematical models of natural phenomena; it plays an important role as a gcritical phenomenon.h That is what I am most interested in. To analyze these, I use the basics of the integral theory, Fourier analysis (real analysis), and functional analysis. I am also interested in some engineering model that can be induced from such a phenomenon as one natural conclusion, and in the study of the numerical solutionbased algorithm.

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Advice on Research 

@@The research we are pursuing is on the model of partial differential equations and the practical examples of them, for which you need to know such tools as of the basics of real analysis and the functional analysis. For that, you are requested to read textbooks of that area, and get used to the associated methods to use. After that, you move on to touch some of the practical equations, and use such methods available. Following the theoretical structure of mathematics, you need to think about which points you clearly can understand, which part is what you do not understand, and how you would be able to clarify what you do not understand well. That is the major subject you must work on.

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Titles of master's theses advised (partial) 

 gEvaluation of Nonlinear Terms of Fluid Mechanics Equations in a halfspaceh
 gAppropriateness for the Initial Problem of Nonlinear Schr?dinger Type Equation of the 4th Order that describes the Dynamics of Vortex Filamenth
 gBMO Algorithm for Mean Curvature Flowh
 gAsymptotic Behavior of the Solution to Initial Value Problem for Semilinear Damped Wave Equationsh
 gSolution to Driftdiffusion Equations for Semiconductor Divse Simulationh
 gHarmack Inequality for a Degenerate Parabolic Equationh

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