Existence for evolutionary Neumann problems with linear growth by stability results

Schätzler L (2019)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2019

Journal

Book Volume: 44

Pages Range: 1055-1092

Journal Issue: 2

DOI: 10.5186/aasfm.2019.4461

Abstract

We are concerned with the Neumann type boundary value problem to parabolic systems

\partial_t u − div(Dξf(x, Du)) = −Dug(x, u),

where u is vector-valued, f satisfies a linear growth condition and ξ \mapsto f(x, ξ) is convex. We prove that variational solutions of such systems can be approximated by variational solutions to

\partial_t u − div(Dξfp(x, Du)) = −Dug(x, u)

with p >1. This can be interpreted both as a stability and existence result for general flows with linear growth.

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APA:

Schätzler, L. (2019). Existence for evolutionary Neumann problems with linear growth by stability results. Annales Academiae Scientiarum Fennicae-Mathematica, 44(2), 1055-1092. https://dx.doi.org/10.5186/aasfm.2019.4461

MLA:

Schätzler, Leah. "Existence for evolutionary Neumann problems with linear growth by stability results." Annales Academiae Scientiarum Fennicae-Mathematica 44.2 (2019): 1055-1092.

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