• Title, Summary, Keyword: global stability

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GLOBAL ATTRACTORS FOR NONLOCAL PARABOLIC EQUATIONS WITH A NEW CLASS OF NONLINEARITIES

  • Anh, Cung The;Tinh, Le Tran;Toi, Vu Manh
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.531-551
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    • 2018
  • In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

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.

A study on relearning program of deep stabilizing muscle for low back pain (요통에 적용된 심부 안정근 재교육 프로그램에 관한 연구)

  • Koo, Hee-Seo;Kim, Soon-Ja
    • The Journal of Korean Physical Therapy
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    • v.16 no.4
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    • pp.11-22
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    • 2004
  • The concept of segmental stabilization has been one of the most exciting advancements in the field of physical therapy. Specific deep stabilizing muscle have proven to reverse motor control deficits that occurs after back injury. After an injury, a new motor programming strategy is adopted and there is excessive recruitment of the large , strong , global muscular system works instead of small segmental deep muscle recruitment for stability. Many physical therapists and doctors mistakenly prescribe therapeutic exercise for low back pain to use larger, superficial musculature to strengthen the spine for stability and pain control. But motor control coordination of local segmental muscle is actually the key to stability and pain control, not strengthening of global muscle. A recent focus in physiotherapy management of patients with chronic back pain has been the specific training of muscles surrounding the lumbar spine whose primary role is considered to be the provision of dynamic stability and segmental control to the spine. These are the deep transverse abdominis muscle and lumbar multifudus.

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Novel Results for Global Exponential Stability of Uncertain Systems with Interval Time-varying Delay

  • Liu, Yajuan;Lee, Sang-Moon;Kwon, Oh-Min;Park, Ju H.
    • Journal of Electrical Engineering and Technology
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    • v.8 no.6
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    • pp.1542-1550
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    • 2013
  • This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

MATHEMATICAL ANALYSIS OF A MULTIFLUID INTERPENETRATION MIX MODEL

  • Jin, Hyeon-Seong
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.319-327
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    • 2012
  • The equations of a multifluid interpenetration mix model are analyzed. The model is an intermediate mix model in the sense that it is defined by partial pressures but only a single global pressure and a single global temperature. It none-the-less avoids the stability difficulty. It is shown that the model is hyperbolic so that it is mathematically stable.

GLOBAL ASYMPTOTIC STABILITY OF A HIGHER ORDER DIFFERENCE EQUATION

  • Hamza, Alaa E.;Khalaf-Allah, R.
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.439-445
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    • 2007
  • The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

QUALITATIVE ANALYSIS OF A DIFFUSIVE FOOD WEB CONSISTING OF A PREY AND TWO PREDATORS

  • Shi, Hong-Bo
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1827-1840
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    • 2013
  • This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the nonexistence of non-constant positive steady states, which gives some descriptions of the effect of diffusion on the pattern formation.

GLOBAL ASYMPTOTIC STABILITY OF POSITIVE STEADY STATES OF AN n-DIMENSIONAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH DIFFUSION

  • Zhou, Jun
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1847-1854
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    • 2013
  • The main concern of this paper is to study the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF POSITIVE ALMOST PERIODIC SOLUTIONS FOR A DELAYED NICHOLSON'S BLOWFLIES MODEL

  • Xu, Yanli
    • Journal of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.473-493
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    • 2014
  • This paper concerns with a class of delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.

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.