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

Ben Andrews; Julie Faye Clutterbuck

doi:10.1016/j.jde.2009.01.024

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

Ben Andrews, Julie Faye Clutterbuck

Research output: Contribution to journal › Article › Research › peer-review

14 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 language	English
Pages (from-to)	4268 - 4283
Number of pages	16
Journal	Journal of Differential Equations
Volume	246
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2009.01.024
Publication status	Published - 2009
Externally published	Yes

Access to Document

10.1016/j.jde.2009.01.024

Cite this

@article{3f92f324f3744094bb2cb200129a4fd2,

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",

issn = "0022-0396",

publisher = "Elsevier",

number = "11",

}

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 -

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

Abstract

Access to Document

Other files and links

Cite this