• Title, Summary, Keyword: global existence

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LOCAL EXISTENCE AND GLOBAL UNIQUENESS IN ONE DIMENSIONAL NONLINEAR HYPERBOLIC INVERSE PROBLEMS

  • Choi, Jong-Sung
    • Communications of the Korean Mathematical Society
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    • v.17 no.4
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    • pp.593-606
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    • 2002
  • We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

REGULARITY OF 3D NAVIER-STOKES EQUATIONS WITH SPECTRAL DECOMPOSITION

  • Jeong, Hyosuk
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.583-592
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    • 2016
  • In this paper, we consider the global existence of strong solutions to the incompressible Navier-Stokes equations on the cubic domain in $R^3$. While the global existence for arbitrary data remains as an important open problem, we here provide with some new observations on this matter. We in particular prove the global existence result when ${\Omega}$ is a cubic domain and initial and forcing functions are some linear combination of functions of at most two variables and the like by decomposing the spectral basis differently.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF A PLATE EQUATION WITH A CONSTANT DELAY TERM AND LOGARITHMIC NONLINEARITIES

  • Remil, Melouka
    • Communications of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.321-338
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    • 2020
  • In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

GLOBAL WEAK SOLUTIONS FOR THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM IN TWO DIMENSIONS

  • Xiao, Meixia;Zhang, Xianwen
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.591-598
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    • 2018
  • This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

  • Zhang, Zhengqiu;Wang, Liping
    • Journal of the Korean Mathematical Society
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    • v.48 no.4
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    • pp.727-747
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    • 2011
  • By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

EXISTENCE AND LONG-TIME BEHAVIOR OF SOLUTIONS TO NAVIER-STOKES-VOIGT EQUATIONS WITH INFINITE DELAY

  • Anh, Cung The;Thanh, Dang Thi Phuong
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.379-403
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    • 2018
  • In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

GLOBAL EXISTENCE FOR VOLTERRA-FREDHOLM TYPE FUNCTIONAL IMPULSIVE INTEGRODIFFERENTIAL EQUATIONS

  • Vijayakumar, V.;Prakash, K. Alagiri;Murugesu, R.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.17 no.1
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    • pp.17-28
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    • 2013
  • In this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type functional impulsive integrodifferential equations. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.