• 제목/요약/키워드: global existence

검색결과 309건 처리시간 0.02초

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

  • Choi, Jong-Sung
    • 대한수학회논문집
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    • 제17권4호
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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
    • 호남수학학술지
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    • 제38권3호
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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
    • 대한수학회논문집
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    • 제35권1호
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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.

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

  • Zhang, Zhengqiu;Wang, Liping
    • 대한수학회지
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    • 제48권4호
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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.

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

  • Xiao, Meixia;Zhang, Xianwen
    • 대한수학회보
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    • 제55권2호
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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.

GLOBAL EXISTENCE OF SOLUTIONS TO THE PREY-PREDATOR SYSTEM WITH A SINGLE CROSS-DIFFUSION

  • Shim, Seong-A
    • 대한수학회보
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    • 제43권2호
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    • pp.443-459
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    • 2006
  • The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $T\;{\leq}\;{\infty}$. By obtaining the bounds of $W\array_2^1$-norms of the local solution independent of T we establish the global existence of the solution. And the long-time behaviors of the global solution are analyzed when the diffusion rates $d_1\;and\;d_2$ are sufficiently large.

GLOBAL ATTRACTOR FOR A SEMILINEAR PSEUDOPARABOLIC EQUATION WITH INFINITE DELAY

  • Thanh, Dang Thi Phuong
    • 대한수학회논문집
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    • 제32권3호
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    • pp.579-600
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    • 2017
  • In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.