Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

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8 Citations (Scopus)

Abstract

We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.
Original languageEnglish
Pages (from-to)4268 - 4283
Number of pages16
JournalJournal of Differential Equations
Volume246
Issue number11
DOIs
Publication statusPublished - 2009
Externally publishedYes

Cite this

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title = "Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable",
abstract = "We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.",
author = "Ben Andrews and Clutterbuck, {Julie Faye}",
year = "2009",
doi = "10.1016/j.jde.2009.01.024",
language = "English",
volume = "246",
pages = "4268 -- 4283",
journal = "Journal of Differential Equations",
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Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable. / Andrews, Ben; Clutterbuck, Julie Faye.

In: Journal of Differential Equations, Vol. 246, No. 11, 2009, p. 4268 - 4283.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

AU - Andrews, Ben

AU - Clutterbuck, Julie Faye

PY - 2009

Y1 - 2009

N2 - We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.

AB - We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.

UR - http://goo.gl/RBe77U

U2 - 10.1016/j.jde.2009.01.024

DO - 10.1016/j.jde.2009.01.024

M3 - Article

VL - 246

SP - 4268

EP - 4283

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 11

ER -