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Convergence of a family of solutions to a Fujita-type equation in domains with cavities

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Abstract

The Dirichlet problem for a Fujita-type equation, i.e., a second-order quasilinear uniformly elliptic equation is considered in domains Ωε with spherical or cylindrical cavities of characteristic size ε. The form of the function in the condition on the cavities’ boundaries depends on ε. For ε tending to zero and the number of cavities increasing simultaneously, sufficient conditions are established for the convergence of the family of solutions {u ε(x)} of this problem to the solution u(х) of a similar problem in the domain Ω with no cavities with the same boundary conditions imposed on the common part of the boundaries ∂Ω and ∂Ωε. Convergence rate estimates are given.

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”, Russian Academy of Sciences, Moscow, 119333, Russia

    S. V. Pikulin

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Correspondence to S. V. Pikulin.

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Original Russian Text © S.V. Pikulin, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 11, pp. 1902–1930.

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Pikulin, S.V. Convergence of a family of solutions to a Fujita-type equation in domains with cavities. Comput. Math. and Math. Phys. 56, 1872–1900 (2016). https://doi.org/10.1134/S0965542516110099

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