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The Cauchy Problem for Nonlinear Parabolic Equations with Lévy Laplacian

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Abstract

A solution to the Cauchy problem for a rather general class of nonlinear parabolic equations involving the infinite-dimensional Laplacian ΔL of the form \(f(U(t,x),\frac{\partial U(t,x)}{\partial t},\Delta_{L}U(t,x))=0\) , where f is a real function defined on R3 is presented.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany, SFB 611, Bonn, BiBoS, Bielefeld-Bonn, CERFIM, Locarno and USI, Switzerland

    S. Albeverio

  2. St. Petersburg State University for Architecture and Civil Engineering, 2-ja Krasnoarmejskaja 4, 190005, St. Petersburg, Russia

    Ya. Belopolskaya

  3. UkrNIIMOD, Bozenko 84, Kiev, GSP 03680, Ukraine

    M. Feller

Authors
  1. S. Albeverio
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  2. Ya. Belopolskaya
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  3. M. Feller
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Mathematics Subject Classifications (2000)

35R15, 46G05.

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Albeverio, S., Belopolskaya, Y. & Feller, M. The Cauchy Problem for Nonlinear Parabolic Equations with Lévy Laplacian. Potential Anal 24, 125–136 (2006). https://doi.org/10.1007/s11118-005-3886-6

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  • DOI: https://doi.org/10.1007/s11118-005-3886-6

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