• 제목/요약/키워드: parabolic

검색결과 1,121건 처리시간 0.031초

UNIQUENESS OF SOLUTIONS FOR A DEGENERATE PARABOLIC EQUATION WITH ABSORPTION

  • Lee, Jin Ho;Jang, Seong Hee
    • Korean Journal of Mathematics
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    • 제5권2호
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    • pp.151-167
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    • 1997
  • We estimate the interior Lipschitz norm and maximum of the solution for degenerate parabolic equations with absorption. Also obtain the growth rate of the solution $u$ in terms of time $t$. From this we show the uniqueness of solution with respect to the initial trace.

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CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX

  • Mi, Yongsheng;Mu, Chunlai;Chen, Botao
    • 대한수학회지
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    • 제48권3호
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    • pp.513-527
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    • 2011
  • The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.

GLOBAL W1,2p ESTIMATES FOR NONDIVERGENCE PARABOLIC OPERATORS WITH POTENTIALS SATISFYING A REVERSE HÖLDER CONDITION

  • Pan, Guixia;Tang, Lin
    • 대한수학회지
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    • 제54권5호
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    • pp.1357-1377
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    • 2017
  • In this article, we first give the $L^p$ boundedness of the operator $D^2L^{-1}$ with BMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator L with VMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition.

ERROR ESTIMATES FOR FULLY DISCRETE DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC EQUATIONS

  • Ohm, Mi-Ray;Lee, Hyun-Yong;Shin, Jun-Yong
    • Journal of applied mathematics & informatics
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    • 제28권3_4호
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    • pp.953-966
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    • 2010
  • In this paper, we develop discontinuous Galerkin methods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite element spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^2(L^2)$ normed space.

FINITE VOLUME ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

  • LI, QIAN;LIU, ZHONGYAN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제6권2호
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    • pp.85-97
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    • 2002
  • In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.

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A PRIORI $L^2$-ERROR ESTIMATES OF THE CRANK-NICOLSON DISCONTINUOUS GALERKIN APPROXIMATIONS FOR NONLINEAR PARABOLIC EQUATIONS

  • Ahn, Min-Jung;Lee, Min-A
    • East Asian mathematical journal
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    • 제26권5호
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    • pp.615-626
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    • 2010
  • In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

EXTINCTION AND POSITIVITY OF SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC EQUATIONS WITH GRADIENT SOURCE TERMS

  • Yi, Su-Cheol
    • 충청수학회지
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    • 제30권4호
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    • pp.397-409
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    • 2017
  • In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

Existence and Behavior Results for a Nonlocal Nonlinear Parabolic Equation with Variable Exponent

  • Sert, Ugur;Ozturk, Eylem
    • Kyungpook Mathematical Journal
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    • 제60권1호
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    • pp.145-161
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    • 2020
  • In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.

FINITE VOLUME ELEMENT METHODS FOR NONLINEAR PARABOLIC INTEGRODIFFERENTIAL PROBLEMS

  • Li, Huanrong;Li, Qian
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제7권2호
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    • pp.35-49
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    • 2003
  • In this paper, finite volume element methods for nonlinear parabolic integrodifferential problems are proposed and analyzed. The optimal error estimates in $L^p\;and\;W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ are obtained. The main results in this paper perfect the theory of FVE methods.

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