| Co-Investigator(Kenkyū-buntansha) |
ONO Akira Kyushu University, College of General Education, Professor., 教養部, 教授 (80038405)
AIZAWA Sadakazu Kobe University, Faculty of Science, Professor., 理学部, 教授 (20030760)
MOCHIZUKI Kiyoshi Shinshu University, Faculty of Science, Professor., 理学部, 教授 (80026773)
MATSUMURA Mutsuhide Tsukuba University, Institute of Mathematics, Professor., 数学系, 教授 (30025879)
AGEMI Rentaro Hokkaido University, Faculty of Science, Professor., 理学部, 教授 (10000845)
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| Research Abstract |
The researches carried out under this Grant-in-Aid for Cooperative Research (A) contain those of the ordinary differential equations, the partial differential equations and the subjects related to two fields. But we report here mainly on the researches in the theory of partial differential equations.
For linear partial differential equations, the systematic researches were carried out in the following subjects : [ <I> ] Cauchy problems (wellposedness for hyperbolic equations, propagation of singularities, equations with complex independent variables, equations of Schrodinger type); [ <II> ] Initial-boundary value problems (parabolic equations, hyperbolic equations and Goursat problem); [ <III> ] Boundary value problems (mainly for elliptic equations, including spectral theory); [ <IV> ] Local theory (uniqueness of solutions, hypeollipticity, pseudo-differential operators); [ <V> ] Scattering theory.
For nonlinear partial differential equations, many substantial works were done in the fol
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lowing subjects : [ <I> ] Elliptic equations (existence of positive solutions, Holder continuity of solutions, variational inequalities); [ <II> ] Parabolic equations (mainly on the existence on the existence of positive global solutions for single or systems of equations and the stability of stationary solutions); [ <III> ] Hyperbolic equations (existence of local or global solutions); [ <IV> ] Fluid dynamics and Boltzmann equation (local or global solutions for the equations of viscous compressible flows, global solutions for Boltzmann equation, weak solutions for Navier-Stokes equation, relationship among the fundamental equations).
Both in 1985 and 1986, we held, once a year, a joint symposium with a great number of participants researching ordinary or partial differential equations. Also, a certain number of conferences of small size were held by leadership of investigators. Briefly, the publications and oral announcements of results, discussions and the exchanges of informations in our field were done very actively in these two years.
On the other hand, the researches of the ordinary differential equations were carried out under the Grant-in-Aid for Cooporative Research (A) headed by Professor Tosihusa Kimura. The activity in this field will be reported by him. Less
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