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Boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian resolved with respect to the derivative

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Ukrainian Mathematical Journal Aims and scope

We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian ∆ L resolved with respect to the derivative

$$ \frac{{\partial U\left( {t,x} \right)}}{{\partial t}} = f\left( {U\left( {t,x} \right),{\Delta_L}U\left( {t,x} \right)} \right) $$

in fundamental domains of a Hilbert space.

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References

  1. M. N. Feller, “Remarks on infinitely dimensional nonlinear hyperbolic equations,” Ukr. Mat. Zh., 52, No. 5, 690–701 (2000).

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Authors and Affiliations

  1. “Resurs” Ukrainian Scientific-Research Institute, Kiev, Ukraine

    M. N. Feller

  2. National University of Biological Resources and Nature Management of Ukraine, Kiev, Ukraine

    I. I. Kovtun

Authors
  1. M. N. Feller
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  2. I. I. Kovtun
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Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 10, pp. 1400–1407, October, 2010.

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Feller, M.N., Kovtun, I.I. Boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian resolved with respect to the derivative. Ukr Math J 62, 1625–1634 (2011). https://doi.org/10.1007/s11253-011-0454-7

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  • DOI: https://doi.org/10.1007/s11253-011-0454-7

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