Attractors of m-Hessian Evolutions

We study the asymptotic behavior of C 2-evolutions u = u(x, t) under a given action of the m-Hessian evolution operators and boundary conditions. We obtain sufficient (close to necessary) conditions for the convergence of solutions to the first initial-boundary value problem for the m-Hessian evolution equations to stationary functions as t → ∞. Bibliography: 18 titles.

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Correspondence to N. M. Ivochkina.

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Dedicated to Professor N. N. Uraltseva

Translated from Problems in Mathematical Analysis 78, January 2015, pp. 103-110.

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Ivochkina, N.M., Filimonenkova, N.V. Attractors of m-Hessian Evolutions. J Math Sci 207, 226–235 (2015). https://doi.org/10.1007/s10958-015-2368-7

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Keywords

  • Parabolic Equation
  • Dirichlet Problem
  • Admissible Solution
  • Heat Operator
  • Nonincreasing Function