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 Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 11, Pages 1902–1930 (Mi zvmmf10488)

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

S. V. Pikulin

Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia

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

Key words: convergence of a family of solutions, nonlinear Fujita-type equation, domains with spherical or cylindrical cavities, convergence rate estimates for solutions.

 Funding Agency Grant Number Russian Foundation for Basic Research 13-01-00923_à Russian Academy of Sciences - Federal Agency for Scientific Organizations 3

DOI: https://doi.org/10.7868/S0044466916110119

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:11, 1872–1900

Bibliographic databases:

UDC: 519.63

Citation: S. V. Pikulin, “Convergence of a family of solutions to a Fujita-type equation in domains with cavities”, Zh. Vychisl. Mat. Mat. Fiz., 56:11 (2016), 1902–1930; Comput. Math. Math. Phys., 56:11 (2016), 1872–1900

Citation in format AMSBIB
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