East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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QUADRATURE METHOD FOR EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS ARISING IN A THERMAL EXPLOSION THEORY

  • Eunkyung Ko (Major in Mathematics, College of Natural Science, Keimyung University)
  • Received : 2023.01.16
  • Accepted : 2023.04.11
  • Published : 2023.05.31
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Abstract

We consider a 1-dimensional reaction diffusion equation with the following boundary conditions arising in a theory of the thermal explosion {-u"(t) = λf(u(t)), t ∈ (0, l), -u'(0) + C(0)u(0) = 0, u'(l) + C(l)u(l) = 0, where C : [0, ∞) → (0, ∞) is a continuous and nondecreasing function, λ > 0 is a parameter and f : [0, ∞) → (0, ∞) is a continuous function. We establish the extension of Quadrature method introduced in [8]. Using this extension, we provide numerical results for models with a typical function of f and C in a thermal explosion theory, which verify the existence, uniqueness and multiplicity results proved in [6].

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Acknowledgement

This work was financially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (NRF-2020R1F1A1A01065912).

References

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