Asymptotic behavior of temperature in a nonlinear radiating, linear absorbing rod of finite length

Pao, C. V.

doi:10.1090/qam/462243

Cited by 5 publications

(2 citation statements)

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“…A fruitful method for the treatment of these equations, both analytically and numerically, is the method of upper and lower solutions and its associated monotone iterations (cf. [4,6,10,[15][16][17][18][19][20]22,23]).…”

Section: Introductionmentioning

confidence: 99%

“…However, in many physical problems such as the heat-conduction problem where the boundary surface of the conduction medium subjects to the Boltzmann fourth-power law of cooling, the nonlinearity occurs at the boundary condition (cf. [5,11,13,19]). Similar nonlinear boundary conditions occur in certain types of gas-liquid interaction problems and in enzyme-substate interaction processes (cf.…”

Section: Introductionmentioning

confidence: 99%

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Finite difference reaction diffusion equations with nonlinear boundary conditions

Pao

1995

Numerical Methods Partial

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This article is concerned with numerical solutions of finite difference systems of reaction diffusion equations with nonlinear internal and boundary reaction functions. The nonlinear reaction functions are of general form and the finite difference systems are for both time-dependent and steady-state problems. For each problem a unified system of nonlinear equations is treated by the method of upper and lower solutions and its associated monotone iterations. This method leads to a monotone iterative scheme for the computation of numerical solutions as well as an existencecomparison theorem for the corresponding finite difference system. Special attention is given to the dynamical property of the time-dependent solution in relation to the steady-state solutions. Application is given to a heat-conduction problem where a nonlinear radiation boundary condition obeying the Boltzmann law of cooling is considered. This application demonstrates a bifurcation property of two steady-state solutions, and determines the dynamic behavior of the time-dependent solution. Numerical results for the heat-conduction problem, including a test problem with known analytical solution, are presented to illustrate the various theoretical conclusions. 0

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