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Bifurcations in reaction-diffusion equations and associated dissipative structures

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Abstract

The paper considers semilinear parabolic equations with conditions dependent on a parameter. A stationary solution of the boundary-value problem is constructed in the neighborhood of the bifurcation value of the parameter. The evolution of the solutions of the Cauchy problem to the bifurcation solution—a spatially nonhomogeneous dissipative structure—is examined.

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References

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Authors
  1. A. A. Belolipetskii
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  2. A. M. Ter-Krikorov
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Additional information

Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 15–30, 1998.

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Belolipetskii, A.A., Ter-Krikorov, A.M. Bifurcations in reaction-diffusion equations and associated dissipative structures. Comput Math Model 10, 339–352 (1999). https://doi.org/10.1007/BF02359085

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  • DOI: https://doi.org/10.1007/BF02359085

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