• 제목/요약/키워드: nonlinear ordinary differential equation

검색결과 84건 처리시간 0.026초

NONLINEAR DIFFERENTIAL INCLUSIONS OF SEMIMONOTONE AND CONDENSING TYPE IN HILBERT SPACES

  • Abedi, Hossein;Jahanipur, Ruhollah
    • 대한수학회보
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    • 제52권2호
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    • pp.421-438
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    • 2015
  • In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.

A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION

  • Fang, Zhong Bo
    • 대한수학회지
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    • 제47권4호
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    • pp.789-804
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    • 2010
  • We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: $$[\mid(w^m)]'\mid^{p-2}(w^m)']'\;+\;{\beta}rw'\;+\;{\alpha}w\;+\;(w^q)'\;=\;0$$ satisfying a specific decay rate: $lim_{r\rightarrow\infty}\;r^{\alpha/\beta}w(r)$ = 0 with $\alpha$ := (p - 1)/[pd-(m+1)(p-1)] and $\beta$:= [q-m(p-1)]/[pd-(m+1)(p-1)]. Here m(p-1) > 1 and m(p - 1) < q < (m+1)(p-1). Such a solution arises naturally when we study a very singular solution for a doubly degenerate equation with nonlinear convection: $$u_t\;=\;[\mid(u^m)_x\mid^{p-2}(u^m)_x]_x\;+\;(u^q)x$$ defined on the half line.

구동 점탄성 벨트의 비선형진동 (Nonlinear Vibration of Running Viscoelastic Belts)

  • 우영주;최연선
    • 한국소음진동공학회논문집
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    • 제13권11호
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    • pp.845-851
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    • 2003
  • The nonlinear vibration of moving viscoelastic belts excited by the eccentricity of pulleys is investigated through experimental and analytical methods. Laboratory measurements demonstrate the nonlinearities in the responses of the belt particularly in the resonance region and with the variation of tension, The measurements of the belt motion are made using noncontact laser sensors. Jump and hysteresis phenomenon are observed experimentally and were studied with a model. which considers the nonlinear relation of belt stretch. An ordinary differential equation is derived as a working form of the belt equation of motion, Numerical results show good agreements with the experimental observations, which demonstrates the nonlinearity of viscoelastic moving belts.

점탄성 벨트의 비선형 진동해석 (Nonlinear Vibration Analysis of Viscoelastic Belts)

  • 우영주;최연선
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2002년도 춘계학술대회논문집
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    • pp.836-841
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    • 2002
  • The nonlinear vibration of moving viscoelastic belts excited by the eccentricity of pulleys is investigated through experimental and analytical methods. Laboratory measurements demonstrate the nonlinearities in the responses of the belt, particularly in the resonance region and with the variation of tension. The measurements of the belt motion were made using a noncontact laser sensor Jump and hysteresis phenomenon are observed experimentally and are studied with a model which considers the nonlinear relation of belt stretch. An ordinary differential equation is derived as a working form of the belt equation of motion. Numerical results show good agreements with the experimental observations, which demonstrates the nonlinearity of viscoelastic moving belts

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OBSERVATIONS ON A FURTHER IMPROVED ($\frac{G}{G}$) - EXPANSION METHOD AND THE EXTENDED TANH-METHOD FOR FINDING EXACT SOLUTIONS OF NONLINEAR PDES

  • Zayed, E.M.E.
    • Journal of applied mathematics & informatics
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    • 제30권1_2호
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    • pp.253-264
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    • 2012
  • In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($\frac{G}{G}$) - expansion method, where $G=G({\xi})$ satisfies the auxiliary ordinary differential equation $[G^{\prime}({\xi})]^2=aG^2({\xi})+bG^4({\xi})+cG^6({\xi})$, where ${\xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).

불규칙적으로 가진되는 동흡진기계의 비선형응답현상 (Nonlinear Response Phenomena of a Randomly Excited Vibration Absorber System)

  • 조덕상
    • 한국산업융합학회 논문집
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    • 제3권2호
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    • pp.141-147
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    • 2000
  • The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

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Application of the Equivalent Frequency Response Method to Runoff Analysis

  • Fujita, Mutsuhiro;Hamouda, Ruai;Tanaka, Gaku
    • 한국수자원학회논문집
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    • 제33권S1호
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    • pp.101-110
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    • 2000
  • This paper introduces the equivalent frequency response method(EFRM) into runoff analysis. This EFRM originally had been developed to analyze dynamic behavior of nonlinear elements such as threshold and saturation in control engineering. Many runoff models are described by nonlinear ordinary of partial differential equations This paper presents that these nonlinear differential equations can be converted into semi-linear ones based on EFRM. The word of "a semi-linear equation" means that the coefficients of derived equations depend on average rainfall.

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Application of the Equivalent Frequency Response Method to Runoff Analysis

  • Mutsuhiro Fujita;Ruai Hamouda;Gaku Tanaka
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2000년도 학술발표회 논문집
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    • pp.1-2
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    • 2000
  • This paper introduces the equivalent frequency response method (EFRM) into runoff analysis. This EFRM originally had been developed to analyze dynamic behavior of nonlinear elements such as threshold and saturation in control engineering. Many runoff models are described by nonlinear ordinary or partial differential equations. This paper presents that these nonlinear differential equations can be converted into semi-linear ones based on EFRM. The word of “a semi-linear equation” means that the coefficients of derived equations depend on average rainfall

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A GENERAL MULTIPLE-TIME-SCALE METHOD FOR SOLVING AN n-TH ORDER WEAKLY NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING

  • Azad, M. Abul Kalam;Alam, M. Shamsul;Rahman, M. Saifur;Sarker, Bimolendu Shekhar
    • 대한수학회논문집
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    • 제26권4호
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    • pp.695-708
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    • 2011
  • Based on the multiple-time-scale (MTS) method, a general formula has been presented for solving an n-th, n = 2, 3, ${\ldots}$, order ordinary differential equation with strong linear damping forces. Like the solution of the unified Krylov-Bogoliubov-Mitropolskii (KBM) method or the general Struble's method, the new solution covers the un-damped, under-damped and over-damped cases. The solutions are identical to those obtained by the unified KBM method and the general Struble's method. The technique is a new form of the classical MTS method. The formulation as well as the determination of the solution from the derived formula is very simple. The method is illustrated by several examples. The general MTS solution reduces to its classical form when the real parts of eigen-values of the unperturbed equation vanish.

ATM용 크라운벨트의 횡진동 해석 (Transverse Vibration of ATM Crown belt)

  • 손영부;최연선
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2007년도 추계학술대회논문집
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    • pp.1212-1217
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    • 2007
  • ATM(automated teller machine) is a machine which can deposit and withdraw money directly. For effective transfer of bills in the machine, crown belts are used. In this paper, the transverse vibration of crown belt is investigated. The equation of motion of the belt is derived using Lagrange's equation. Galerkin's method is applied to convert the partial differential equation to the ordinary differential equations. Experimental investigations are performed on the belt system with the variation of pulley type, eccentricity, and tension. The results of numerical analysis show in good agreement with the experimental results.

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