Semigroups of Locally Lipschitzian Operators and applications
Project/Area Number  04640137 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
解析学

Research Institution  Niigata University 
Principal Investigator 
KOBAYASHI Yoshikazu Niigata Univ. Eng. Prof., 工学部, 教授 (80092691)

CoInvestigator(Kenkyūbuntansha) 
KAJIKIYA Ryuji Niigata Univ. Eng. Associate Prof., 工学部, 助教授 (10183261)

Project Period (FY) 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1993 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1992 : ¥400,000 (Direct Cost : ¥400,000)

Keywords  evolution equation / semigroups / dissipative operator / elliptic equations / radical solution / zero of solution / 非線形発展方程式 / Osgoodの条件 / マイルド解 / 半線形楕円型方程式 / 漸近挙動 
Research Abstract 
1. The existence of radial solutions for the semilinear Laplace equations in R^n is proved and the asymptotic behavior of the solutions is investigated. The elliptic equation with the nonlinear term f(u)=*u*^<p1>u (*u*(〕SY.gtoreq.〔)1), =*u*^<q1>u (*u*<1), where 1<p<(n+2)/(n2)<q, is studied and it is shown that any radial solution behaves, as *chi*>*, like either (i)c*chi*^<(n2)> or (ii)(〕SY.+.〔)c^<**>*chi*^<2/(q1)>. 2. The more general nonlinear term than the above f(u) is considered and the Dirichlet problem of the elliptic equations in symmetric domains ; annulus, ball, exterior of ball and R^n are investigated. The existence of radial solution having exactly kappa zeros in 0(〕SY.ltoreq.〔)*chi*<* is proved for each domain and any integer kappa(〕SY.gtoreq.〔)0. The result gives a weak sufficient condision on the nonlinear term for the existence of radial solutions. 3. The existence of weak solutions of nonlinear KleinGordon equations, FitzHughNagumo equations and two dimensional NavierStokes equations is shown to be proved by using an unified abstract theory of semigroups of nonlinear locally Lipschitzian operators. 4. A class of generalized dissipative operators is introduced and the existence and the convergence of difference approximate solutions of abstract Cauchy problems for the operation in the class are shown. Both of the known theory ofgeneration of semigroups and the typical uniquely existence theorems of solutions of ordinary differential equations are extended.

Report
(3results)
Research Output
(14results)