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    Weighted in time energy estimates for parabolic equations with applications to non-linear and non-local problems

    191234_191234.pdf (667.0Kb)
    Access Status
    Open access
    Authors
    Dokuchaev, Nikolai
    Date
    2012
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Dokuchaev, Nikolai. 2012. Weighted in time energy estimates for parabolic equations with applications to non-linear and non-local problems. Dynamics of Partial Differential Equations. 9 (4): pp. 369-381.
    Source Title
    Dynamics of Partial Differential Equations
    DOI
    10.4310/DPDE.2012.v9.n4.a4
    ISSN
    1548159X
    Remarks

    First published in Dynamics of Partial Differential Equations, in Volume 9, Issue 4, 2012, published by International Press

    URI
    http://hdl.handle.net/20.500.11937/7636
    Collection
    • Curtin Research Publications
    Abstract

    The paper suggests a modification of the contracting mapping method for non-linear and non-local parabolic equations. This modification is based on weighted in time energy estimates for the L2-norm of the solution of a parabolic equation via a weighted version of the H^-1-norm of the free term such that the inverse matrix of the higher order coefficients of the parabolic equation is included into the weight. More precisely, this estimate represents the upper estimate that can be achieved via transformation of the equation by adding a constant to the zero order coefficient. The limit constant in this estimate is independent from the choice of the dimension, domain, and the coefficients of the parabolic equation.

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