Oscillation of Neural Type Nonlinear Impulsive Hyperbolic Equations with Several Delays

2013 ◽  
Vol 275-277 ◽  
pp. 843-847
Author(s):  
Li Xiao ◽  
Ji Chen Yang ◽  
Guang Jie Liu ◽  
An Ping Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Several Delays ◽  
Oscillatory Properties

In this paper, oscillatory properties of solutions for neutral type nonlinear impulsive hyperbolic partial differential equations with several delays are investigated and a series of sufficient conditions for oscillation of the equations are established.

scholarly journals On local equivalence for vector field systems

1990 ◽  
Vol 42 (2) ◽  
pp. 215-229 ◽  
Author(s):  
P.J. Vassiliou
Keyword(s):  
Vector Field ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Contact Structure ◽  
Sufficient Conditions ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
General Integral ◽  
Field Systems ◽  
Local Equivalence

We give sufficient conditions for C∞ vector field systems on Rn with genus g = 1 to be diffeomorphic to a contact structure. The diffeomorphism is explicitly constructed and used to give the most general integral submanifolds for the systems. Finally the implications of these results for integrable hyperbolic partial differential equations in the plane is discussed.

scholarly journals Wendroff type inequalities for nonlinear hyperbolic equations

2001 ◽  
Vol 32 (4) ◽  
pp. 327-333
Author(s):  
Wen Rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Hyperbolic Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Nonlinear Hyperbolic Equations ◽  
Initial Value ◽  
Partial Differential

Several Wendroff type inequalities are derived, and applications to characteristic initial value problems involving hyperbolic partial differential equations are illustrated.

Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients

2015 ◽  
Vol 25 (7) ◽  
pp. 1574-1589 ◽  
Author(s):  
Anjali Verma ◽  
Ram Jiwari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Differential Quadrature ◽  
Hyperbolic Partial Differential Equations ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic Equations ◽  
Partial Differential ◽  
Content Type

Purpose – The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM). Design/methodology/approach – The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings – The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that the present numerical technique gives better results than the others. Second, the proposed algorithm gives good accuracy by using very less grid point and less computation cost as comparison to other numerical methods such as finite difference methods, finite elements methods, etc. Originality/value – The author extends CDQM proposed in (Korkmaz and Dağ, 2009b) for two-dimensional nonlinear hyperbolic partial differential equations. This work is new for two-dimensional nonlinear hyperbolic partial differential equations.

scholarly journals Oscillations of certain partial differential equations with deviating arguments

1992 ◽  
Vol 46 (3) ◽  
pp. 373-380 ◽  
Author(s):  
B.S. Lalli ◽  
Y.H. Yu ◽  
B.T. Cui
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Smooth Boundary ◽  
Hyperbolic Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Piecewise Smooth Boundary ◽  
Deviating Arguments ◽  
Image Position ◽  
Oscillation Of Solutions

Sufficient conditions are established for the oscillation of solutions of hyperbolic equations of neutral type of the formwhere R+ = {0, ∞), Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω.

Hyperbolic Partial Differential Equations with Nonlocal Mixed Boundary Values and their Analytic Approximate Solutions

2017 ◽  
Vol 15 (02) ◽  
pp. 1850003 ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Equations ◽  
Mixed Boundary ◽  
Meshfree Method ◽  
Approximate Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
Algebraic Equations ◽  
Partial Differential ◽  
And Performance

Partial differential equations of hyperbolic type when considered with mixed Dirichlet/Neumann constraints as well as nonlocal conservation conditions model many physical phenomena. The prime motivation of the current work is to apply the recently developed meshfree method to such differential equations. The scheme is built on series expansion of the solution via proper base functions akin to the Galerkin approach. In many cases, the simple polynomials are adequate to convert the hyperbolic partial differential equation and boundary conditions of nonlocal kind into easily treatable algebraic equations concerning the coefficients of the series. If the sought solutions are polynomials of any degree, then the method has the ability of resolving the equations in an exact manner. The validity, applicability, accuracy and performance of the method are illustrated on some well-analyzed hyperbolic equations available in the open literature.

scholarly journals Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

2019 ◽  
Vol 52 (1) ◽  
pp. 482-489 ◽  
Author(s):  
Andriy Bandura ◽  
Oleh Skaskiv ◽  
Liana Smolovyk
Keyword(s):  
Partial Differential Equations ◽  
Continuous Function ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Positive Continuous Function ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Fixed Direction

AbstractIn the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈ℂ} for an arbitrary z0 ∈ℂn and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈ ℤ+) (∀z ∈ ℂn) the following inequality holds{{\left| {\partial _{\bf{b}}^mF(z)} \right|} \over {m!{L^m}(z)}} \le \mathop {\max }\limits_{0 \le k \le {m_0}} {{\left| {\partial _{\bf{b}}^kF(z)} \right|} \over {k!{L^k}(z)}},where L : ℂn → ℝ+ is a positive continuous function, {\partial _{\bf{b}}}F(z) = {d \over {dt}}F\left( {z + t{\bf{b}}} \right){|_{t = 0}},\partial _{\bf{b}}^pF = {\partial _{\bf{b}}}\left( {\partial _{\bf{b}}^{p - 1}F} \right)for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Di Xu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Riccati Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

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