scholarly journals On blowing-up solutions for multi-time nonlinear hyperbolic equations and systems

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2599-2609
Author(s):  
B. Ahmad ◽  
A. Alsaedi ◽  
E. Cuesta ◽  
M. Kirane
Keyword(s):  
Nonlinear Equation ◽  
Hyperbolic Equation ◽  
Space Dimension ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equation ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic Equations ◽  
Blowing Up ◽  
Time Order ◽  
Blowing Up Solutions

For a two-dimensional time nonlinear hyperbolic equation with a power nonlinearity, a threshold exponent depending on the space dimension is presented. Furthermore, the analysis is extended not only to a system of two equations but also to a two-time fractional nonlinear equation with different time order derivatives.

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

scholarly journals On Behavior of Solution of Degenerated Hyperbolic Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Tahir Gadjiev ◽  
Rafig Rasulov ◽  
Orkhan Aliev
Keyword(s):  
Hyperbolic Equation ◽  
Nonlinear Equations ◽  
Finite Time ◽  
Hyperbolic Equations ◽  
Initial Conditions ◽  
Local Existence ◽  
Hyperbolic Type ◽  
Nonlinear Hyperbolic Equations

The purpose of this paper is to learn some features of hyperbolic type of nonlinear equations. It is shown that the solution of the equation approaches to the endlessness in the inside of some initial conditions and time of the special marks. The local existence of the equation’s solution has been proved and the problem of unlimited increasing on the solution of nonlinear hyperbolic equations type during the finite time is investigated.

scholarly journals On Behaviors of the Energy of Solutions for Some Damped Nonlinear Hyperbolic Equations with p-Laplacian

2016 ◽  
Vol 6 ◽  
pp. 13-20
Author(s):  
Soufiane Mokeddem
Keyword(s):  
Decay Rate ◽  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Integral Inequalities ◽  
Nonlinear Hyperbolic Equations ◽  
Rate Estimate

In this paper we are concerned with nonlinear damped hyperbolic equation withp-Laplace of the formutt-Δpu+ σ(t)(ut-Δut)+w|u|m-2u= |u|r-2u.Used the multiplier techniques combined with a nonlinear integral inequalities given by Martinez we established a decay rate estimate for the energy.

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 Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1483
Author(s):  
Shanqin Chen
Keyword(s):  
Large Time ◽  
Hyperbolic Equations ◽  
Strong Stability ◽  
Matrix Exponential ◽  
Linear Component ◽  
Nonlinear Hyperbolic Equations ◽  
Time Step ◽  
Integrating Factor ◽  
The Matrix ◽  
Runge Kutta

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method.

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