• Title, Summary, Keyword: Nonlocal condition

Search Result 61, Processing Time 0.029 seconds

Existence and Uniqueness of Solutions for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory

  • Kwun, Young-Chel;Park, Jong-Seo;Kim, Seon-Yu;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.6 no.4
    • /
    • pp.288-292
    • /
    • 2006
  • Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_{N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_{N}$.

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

  • Mu, Chunlai;Liu, Dengming;Zhou, Shouming
    • Journal of the Korean Mathematical Society
    • /
    • v.47 no.6
    • /
    • pp.1317-1328
    • /
    • 2010
  • In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.

SOME TYPES OF REACTION-DIFFUSION SYSTEMS WITH NONLOCAL BOUNDARY CONDITIONS

  • Han, Yuzhu;Gao, Wenjie
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.6
    • /
    • pp.1765-1780
    • /
    • 2013
  • This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

SEMILINEAR NONLOCAL DIFFERENTIAL EQUATIONS WITH DELAY TERMS

  • Jeong, Jin-Mun;Cheon, Su Jin
    • Journal of the Korean Mathematical Society
    • /
    • v.50 no.3
    • /
    • pp.627-639
    • /
    • 2013
  • The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.