Oscillation Criteria of Impulsive Neutral Parabolic Equations with Nonlinear Diffusion Coefficient
نویسندگان
چکیده
In 1991, the first paper on impulsive partial differential equations [1] was published. For an excellent exposition of this paper and its applications, see [2]. The oscillation theory of impulsive partial differential equations have wide applications in such subjects as control theory, meteorology, biology, medicine, engineering, chemistry and physics. Many results can be found [3-14]. However, there is little in the way of results for impulsive partial differential equations with nonlinear diffusion coefficient (see only [7, 13-14]). In this paper, we study the oscillation of solutions for a class of impulsive neutral delay parabolic equations with nonlinear diffusion coefficient (1) under the boundary conditions (2) and obtain some interesting results for oscillation of the equations. ⎧⎨⎩ ∂ ∂t (u(t, x) + c(t)u(t− τ, x)) = a(t)h(u(t, x))Δu(t, x) + m ∑
منابع مشابه
Forced Oscillation of Neutral Impulsive Parabolic Partial Differential Equations with Continuous Distributed Deviating Arguments
This paper investigated oscillatory properties of solutions for nonlinear parabolic equations with impulsive effects under two different boundary conditions. By using integral averaging method, variable substitution and functional differential inequalities, we established several sufficient conditions. At last, we provided two examples to illustrate the results.
متن کاملOscillation properties for parabolic equations of neutral type
In the last few years there has been much interest in studying the oscillatory behaviour of solutions of partial differential equations with deviating arguments. We refer the reader to Mishev & Bainov [1], [2], Yoshida [3], Georgiou & Kreith [4] and Cui [5]. However, only the papers [1] and [5] considered the oscillation for parabolic differential equations of neutral type. The purpose of this ...
متن کاملLeighton–Coles–Wintner Type Oscillation Criteria for Half-Linear Impulsive Differential Equations
In this paper, we obtain new oscillation criteria for second-order half-linear impulsive differential equations having fixed moments of impulse actions. We also generalize the results to nonlinear impulsive equations. The oscillation criteria obtained in this paper can be considered as extensions of those given by Leighton, (J. London Math. Soc. 27 (1952)), Coles (Proc. Amer. Math. Soc. 19 (196...
متن کاملA Survey on Oscillation of Impulsive Ordinary Differential Equations
This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.
متن کاملAsymptotic Behavior of Solutions of Nonlinear Neutral Delay Forced Impulsive Differential Equations with Positive and Negative Coefficients
Sufficient conditions are obtained for every solution of first order nonlinear neutral delay forced impulsive differential equations with positive and negative coefficients tends to a constant as t ∞.
متن کامل