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dc.contributor.authorDokuchaev, Nikolai
dc.date.accessioned2017-01-30T11:01:18Z
dc.date.available2017-01-30T11:01:18Z
dc.date.created2013-04-01T20:00:50Z
dc.date.issued2012
dc.identifier.citationDokuchaev, 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.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/7636
dc.identifier.doi10.4310/DPDE.2012.v9.n4.a4
dc.description.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.

dc.publisherInternational Press
dc.subjectparabolic equations
dc.subjectnonlinear equations
dc.subjectnon-local equations
dc.subjectregularity
dc.titleWeighted in time energy estimates for parabolic equations with applications to non-linear and non-local problems
dc.typeJournal Article
dcterms.source.volume9
dcterms.source.number4
dcterms.source.startPage369
dcterms.source.endPage381
dcterms.source.issn1548159X
dcterms.source.titleDynamics of Partial Differential Equations
curtin.note

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

curtin.department
curtin.accessStatusOpen access


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