scholarly journals Correction to: Coupled System of Nonlinear Hyperbolic Equations with Variable-Exponents: Global Existence and Stability

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Oulia Bouhoufani ◽  
Ilhem Hamchi
Keyword(s):  
Global Existence ◽  
Hyperbolic Equations ◽  
Coupled System ◽  
Variable Exponents ◽  
Nonlinear Hyperbolic Equations ◽  
Existence And Stability

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.

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.

Mathematical analysis of a tumor invasion model—global existence and stability

2021 ◽  
Vol 61 ◽  
pp. 103297
Author(s):  
Xueyan Tao ◽  
Yuanwei Qi ◽  
Shulin Zhou
Keyword(s):  
Global Existence ◽  
Mathematical Analysis ◽  
Tumor Invasion ◽  
Existence And Stability ◽  
Invasion Model

GLOBAL SOLUTION AND STABILITY FOR SOME NONLINEAR HYPERBOLIC EQUATIONS

1988 ◽  
Vol 21 (3) ◽  
Author(s):  
Zbigniew Koszela ◽  
Roman Stankiewicz
Keyword(s):  
Global Solution ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equations

On global solution of nonlinear hyperbolic equations

1968 ◽  
Vol 30 (2) ◽  
pp. 148-172 ◽  
Author(s):  
D. H. Sattinger
Keyword(s):  
Global Solution ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equations
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