• Title/Summary/Keyword: Nonlinear equations

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A HYBRID METHOD FOR HIGHER-ORDER NONLINEAR DIFFUSION EQUATIONS

  • KIM JUNSEOK;SUR JEANMAN
    • Communications of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.179-193
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    • 2005
  • We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing up an inclined plane. Equations of the type $h_t+f_y(h) = -{\in}^3{\nabla}{\cdot}(M(h){\nabla}{\triangle}h)$ arise in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, t) is the fluid film height. A hybrid scheme is constructed for the solution of two-dimensional higher-order nonlinear diffusion equations. Problems in the fluid dynamics of thin films are solved to demonstrate the accuracy and effectiveness of the hybrid scheme.

Critical Reynolds Number for the Occurrence of Nonlinear Flow in a Rough-walled Rock Fracture (암반단열에서 비선형유동이 발생하는 임계 레이놀즈수)

  • Kim, Dahye;Yeo, In Wook
    • Economic and Environmental Geology
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    • v.52 no.4
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    • pp.291-297
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    • 2019
  • Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.

ITERATIVE ALGORITHMS FOR A FUZZY SYSTEM OF RANDOM NONLINEAR EQUATIONS IN HILBERT SPACES

  • Salahuddin, Salahuddin
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.333-352
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    • 2017
  • In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

ITERATIVE ALGORITHMS FOR A SYSTEM OF RANDOM NONLINEAR EQUATIONS WITH FUZZY MAPPINGS

  • Kim, Jong Kyu;Salahuddin, Salahuddin
    • East Asian mathematical journal
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    • v.34 no.3
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    • pp.265-285
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    • 2018
  • The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

STABILITY PROPERTIES IN NONLINEAR DISCRETE VOLTERRA EQUATIONS WITH UNBOUNDED DELAY

  • Choi, Sung Kyu;Kim, Yunhee;Koo, Namjip;Yun, Chanmi
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.1
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    • pp.197-211
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    • 2013
  • We study some stability properties in discrete Volterra equations by employing to change Yoshizawa's results in [13] for the nonlinear equations into results for the nonlinear discrete Volterra equations with unbounded delay.

A General System of Nonlinear Functional Equations in Non-Archimedean Spaces

  • Ghaemi, Mohammad Bagher;Majani, Hamid;Gordji, Madjid Eshaghi
    • Kyungpook Mathematical Journal
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    • v.53 no.3
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    • pp.419-433
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    • 2013
  • In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.

NEW EXACT TRAVELLING WAVE SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS

  • Lee, Youho;An, Jaeyoung;Lee, Mihye
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.359-370
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    • 2011
  • In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.

BOUNDARY VALUE PROBLEM FOR A CLASS OF THE SYSTEMS OF THE NONLINEAR ELLIPTIC EQUATIONS

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.17 no.1
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    • pp.67-76
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    • 2009
  • We show the existence of at least two nontrivial solutions for a class of the systems of the nonlinear elliptic equations with Dirichlet boundary condition under some conditions for the nonlinear term. We obtain this result by using the variational linking theory in the critical point theory.

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APPLICATION OF FIXED POINT THEOREM FOR UNIQUENESS AND STABILITY OF SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRAL EQUATIONS

  • GUPTA, ANIMESH;MAITRA, Jitendra Kumar;RAI, VANDANA
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.1-14
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    • 2018
  • In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.