Ill-posedness of nonlinear parabolic equation with critical initial condition

Xu Runzhang and Liu Yacheng

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 7, 1363-1374

Abstract: We study the initial boundary value problem of strongly nonlinear parabolic equation:∂u∂t=∑i=1N∂∂xi∂u∂xip−2∂u∂xi+u1+αwith critical initial data. By introducing a family of potential wells the global nonexistence of solution is proved, which solves the open problem existing in some classical literature.

Keywords: Nonlinear parabolic equation; Critical initial data; Potential wells; Global nonexistence (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:7:p:1363-1374

DOI: 10.1016/j.matcom.2010.09.009

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