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dc.contributor.authorBoccardo, Lucio ( )
dc.contributor.authorGallouet, Thierry ( )
dc.contributor.authorVazquez, Juan Luis ( )
dc.identifier.citationBoccardo, L., Gallouet, T., & Vazquez, J. L. (2001). Solutions of nonlinear parabolic equations without growth restrictions on the data. Electronic Journal of Differential Equations, 2001(60), pp. 1-20.en_US

The purpose of this paper is to prove the existence of solutions for certain types of nonlinear parabolic partial differential equations posed in the whole space, when the data are assumed to be merely locally integrable functions, without any control of their behaviour at infinity. A simple representative example of such an equation is

ut - Δu + |u|s-1 u = ƒ,

which admits a unique globally defined weak solution u(x,t) if the initial function u(x,0) is a locally integrable function of x ∈ ℝN and t ∈ [0,T] whenever the exponent s is larger than 1. The results extend to parabolic equations. They have no equivalent for linear or sub-linear zero-order nonlinearities.

dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear parabolic equationsen_US
dc.subjectGlobal existenceen_US
dc.subjectGrowth conditionsen_US
dc.titleSolutions of Nonlinear Parabolic Equations Without Growth Restrictions on the Dataen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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