Numerical solution of initial-boundary system of nonlinear hyperbolic equations

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, Mohamed; Hafez, Ramy M.

doi:10.1007/s13226-015-0152-5

Cited by 4 publications

(1 citation statement)

References 43 publications

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“…They are suitable for evaluating the eect of nonlinearity on the wave speeds. Systems of nonlinear hyperbolic equations have been investigated by many authors, among whom we cite [51,52,53,54]. In the following two sections we nd solutions to our equations under some initial and boundary conditions using either Poincaré expansion or by numerical techniques.…”

Section: Dimension Analysismentioning

confidence: 99%

One-dimensional nonlinear model of generalized thermo-electroelasticity

Ghaleb

Ahmed²,

Mosharafa

2023

Preprint

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We investigate a one-dimensional restriction of a nonlinear model of thermo-electroelasticity in extended thermodynamics and in the quasi-electrostatic regime (see [25]). An additional dependence of the thermal conductivity and the thermal relaxation time on temperature and heat flux is introduced. The aim of the present work is to assess the effect of some quadratic nonlinear couplings between the mechanical, thermal and electric fields. Such couplings are known to have a crucial effect on the stability of the solutions. It is confirmed that there are two speeds of wave propagation of disturbances, the coupled thermoelastic wave and the heat wave. Formulae are provided for both speeds, showing their explicit dependence on temperature, heat flux and electric field. The purely thermal case is briefly considered. The present results may be useful for the description of a broad range of interactions in polarizable materials and for the design of such materials.

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Section: Dimension Analysismentioning

confidence: 99%

One-dimensional nonlinear model of generalized thermo-electroelasticity

Ghaleb

Ahmed²,

Mosharafa

2023

Preprint

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show abstract

One-dimensional nonlinear model of generalized thermo-electroelasticity

2023

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We investigate a one-dimensional restriction of a nonlinear model of thermo-electroelasticity in extended thermodynamics and in the quasi-electrostatic regime (see Ghaleb et al. in Int J Eng Sci 119:29–39, 2017. https://doi.org/10.1016/j.ijengsci.2017.06.010). An additional dependence of the thermal conductivity and the thermal relaxation time on temperature and heat flux is introduced. The aim of the present work is to assess the effect of some quadratic nonlinear couplings between the mechanical, thermal and electric fields. Such couplings are known to have a crucial effect on the stability of the solutions. It is confirmed that there are two speeds of wave propagation of disturbances, the coupled thermoelastic wave and the heat wave. Formulae are provided for both speeds, showing their explicit dependence on temperature, heat flux and electric field. The purely thermal case is briefly considered. The present results may be useful for the description of a broad range of interactions in large polarizable slabs of electro-thermoelastic materials and for the design of such materials.

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Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

Hafez

2018

Comp. Appl. Math.

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Numerical solution of initial-boundary system of nonlinear hyperbolic equations

Cited by 4 publications

References 43 publications

One-dimensional nonlinear model of generalized thermo-electroelasticity

One-dimensional nonlinear model of generalized thermo-electroelasticity

One-dimensional nonlinear model of generalized thermo-electroelasticity

Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

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