• Title, Summary, Keyword: generalized solution

Search Result 479, Processing Time 0.058 seconds

REMARKS ON UNIQUENESS AND BLOW-UP CRITERION TO THE EULER EQUATIONS IN THE GENERALIZED BESOV SPACES

  • Ogawa, Takayoshi;Taniuchi, Yasushi
    • Journal of the Korean Mathematical Society
    • /
    • v.37 no.6
    • /
    • pp.1007-1019
    • /
    • 2000
  • In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

  • PDF

A STRONG SOLUTION FOR THE WEAK TYPE II GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS

  • Kim, Won-Kyu;Kum, Sang-Ho
    • Bulletin of the Korean Mathematical Society
    • /
    • v.43 no.3
    • /
    • pp.599-610
    • /
    • 2006
  • The aim of this paper is to give an existence theorem for a strong solution of generalized vector quasi-equilibrium problems of the weak type II due to Hou et al. using the equilibrium existence theorem for 1-person game, and as an application, we shall give a generalized quasivariational inequality.

Generalized Sensitivity Analysis at a Degenerate Optimal Solution (퇴화최적해에서 일반감도분석)

  • 박찬규;김우제;박순달
    • Journal of the Korean Operations Research and Management Science Society
    • /
    • v.25 no.4
    • /
    • pp.1-14
    • /
    • 2000
  • The methods of sensitivity analysis for linear programming can be classified in two types: sensitivity analysis using an optimal solution, and sensitivity analysis using an approximate optimal solution. As the methods of sensitivity analysis using an optimal solution, there are three sensitivity analysis methods: sensitivity analysis using an optimal basis, positive sensitivity analysis, and optimal partition sensitivity analysis. Since they may provide different characteristic regions under degeneracy, it is not easy to understand and apply the results of the three methods. In this paper, we propose a generalized sensitivity analysis that can integrate the three existing methods of sensitivity analysis. When a right-hand side or a cost coefficient is perturbed, the generalized sensitivity analysis gives different characteristic regions according to the controlling index set that denotes the set of variables allowed to have positive values in optimal solutions to the perturbed problem. We show that the three existing sensitivity analysis methods are special cases of the generalized sensitivity analysis, and present some properties of the generalized sensitivity analysis.

  • PDF

EXISTENCE OF SOLUTION OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS IN GENERAL BANACH SPACES

  • Jeong, Jin-Gyo;Shin, Ki-Yeon
    • Communications of the Korean Mathematical Society
    • /
    • v.11 no.4
    • /
    • pp.1003-1013
    • /
    • 1996
  • The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

  • PDF

GENERALIZED DIFFERENCE METHODS FOR ONE-DIMENSIONAL VISCOELASTIC PROBLEMS

  • Li, Huanrong
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.9 no.2
    • /
    • pp.55-64
    • /
    • 2005
  • In this paper, generalized difference methods(GDM) for one-dimensional viscoelastic problems are proposed and analyzed. The new initial values are given in the generalized difference scheme, so we obtain optimal error estimates in $L^p$ and $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.

  • PDF

COMMON SOLUTION TO GENERALIZED MIXED EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM FOR A NONEXPANSIVE SEMIGROUP IN HILBERT SPACE

  • DJAFARI-ROUHANI, BEHZAD;FARID, MOHAMMAD;KAZMI, KALEEM RAZA
    • Journal of the Korean Mathematical Society
    • /
    • v.53 no.1
    • /
    • pp.89-114
    • /
    • 2016
  • In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

APPROXIMATION OF SOLUTIONS OF A GENERALIZED VARIATIONAL INEQUALITY PROBLEM BASED ON ITERATIVE METHODS

  • Cho, Sun-Young
    • Communications of the Korean Mathematical Society
    • /
    • v.25 no.2
    • /
    • pp.207-214
    • /
    • 2010
  • In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

APPROXIMATION OF SOLUTIONS FOR GENERALIZED WIENER-HOPF EQUATIONS AND GENERALIZED VARIATIONAL INEQUALITIES

  • Gu, Guanghui;Su, Yongfu
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.1_2
    • /
    • pp.465-472
    • /
    • 2010
  • The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].