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The Maximal Regularity of Nonlinear Second-Order Hyperbolic Boundary Differential Equations
AxiomsIn this paper, we show the maximal regularity of nonlinear second-order hyperbolic boundary differential equations. We aim to show if the given second-order partial differential operator satisfies the specific ellipticity condition; additionally, if ...
Xingyu Liu
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Difference methods for nonlinear first-order hyperbolic systems of equations [PDF]
Mathematics of Computation, 1970 Two difference methods for approximating some first-order nonlinear hyperbolic differential equations are considered. The methods apply to problems arising in a number of physical applications. Each of the methods is explicit and can be implemented on a computer easily. It is proved that the methods are first-order convergent in the maximum norm.
Shampine, L. F., Thompson, R. J.
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A comprehensive analytical study of solitons and nonlinear dynamics in a concatenated DNLS-type model [PDF]
Scientific ReportsIn mathematical physics, such as nuclear physics, fluid dynamics, quantum optics, and plasma physics, nonlinear evolution equations are essential. The concatenation model, that was first presented in 2014 and has attracted a lot of interest in nonlinear ...
Fozia Bashir Farooq +4 more
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Demonstratio Mathematica, 2023 In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference.
Lei Weidong +4 more
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Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity
Axioms, 2021 This work aims to obtain new transformations and auto-Bäcklund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives.
Tatyana V. Redkina +3 more
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Nonlinear Engineering, 2023 Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform ...
Kapoor Mamta
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Finite element method for nonlocal problems of Kirchhoff-type in domains with moving boundary
Scientific African, 2022 This paper is devoted to the analysis of the finite element method for the mixed problem for the Kirchhoff nonlinear model given by the hyperbolic-parabolic equations in a bounded noncylindrical domain with moving boundaries.
M. Mbehou +2 more
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Mathematics, 2022 The study considers a nonlinear multi-parameter reaction–diffusion system of two Lotka–Volterra-type equations with several delays. It treats both cases of different diffusion coefficients and identical diffusion coefficients.
Andrei D. Polyanin, Alexei I. Zhurov
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Biomath, 2021 The numerical method for simulation dynamics of nonlinear epidemic model of age-structured sub-populations of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) is developed (SIPCV model ...
Vitalii Akimenko, Fajar Adi-Kusumo
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Estimation of Cauchy data for a first-order nonlinear hyperbolic equation
Journal of Mathematical Analysis and Applications, 1988 The authors study the Cauchy problem: \[ u_ t+uu_ x+au=\phi(x,t)\text{ in } \Omega \times (0,t),\;u(x,0)=u_ 0(x), \] where \(\Omega\) is an open interval in \({\mathbb{R}}\). This system is associated with an initial value problem for the system: \[ dx/dt=z,\quad dz/dt=-az+\phi (x,t). \] Suppose that M observations \(\{z_ k\}^ M_{k=1}\) at positions \(\
Grasse, Kevin A, White, L.W
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