Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations

B. Cockburn; G. Gripenberg; S. O. Londen

doi:10.1006/jdeq.2000.3802

Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations

B. Cockburn, G. Gripenberg, S. O. Londen

School of Mathematics

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

8 Scopus citations

Abstract

This paper establishes an upper bound for u-v where u is a subsolution of u_t+F(u, D_xu, D²_xu)=0and v is a supersolution ofv_t+G(v, D_xv, D²_xv)=0in (0, ∞)×Ω with Neumann boundary conditions and where Ω is an open convex set.

Original language	English (US)
Pages (from-to)	180-187
Number of pages	8
Journal	Journal of Differential Equations
Volume	170
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.2000.3802
State	Published - Feb 10 2001

Bibliographical note

Funding Information:
1Partially supported by the National Science Foundation (Grant DMS-9806956).

Publisher link

10.1006/jdeq.2000.3802

Find It

Find It at U of M Libraries

Cite this

@article{d348c26694e841f89106da2a561b2361,

title = "Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations",

abstract = "This paper establishes an upper bound for u-v where u is a subsolution of ut+F(u, Dxu, D2xu)=0and v is a supersolution ofvt+G(v, Dxv, D2xv)=0in (0, ∞)×Ω with Neumann boundary conditions and where Ω is an open convex set.",

author = "B. Cockburn and G. Gripenberg and Londen, {S. O.}",

note = "Funding Information: 1Partially supported by the National Science Foundation (Grant DMS-9806956).",

year = "2001",

month = feb,

day = "10",

doi = "10.1006/jdeq.2000.3802",

language = "English (US)",

volume = "170",

pages = "180--187",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations

AU - Cockburn, B.

AU - Gripenberg, G.

AU - Londen, S. O.

N1 - Funding Information: 1Partially supported by the National Science Foundation (Grant DMS-9806956).

PY - 2001/2/10

Y1 - 2001/2/10

N2 - This paper establishes an upper bound for u-v where u is a subsolution of ut+F(u, Dxu, D2xu)=0and v is a supersolution ofvt+G(v, Dxv, D2xv)=0in (0, ∞)×Ω with Neumann boundary conditions and where Ω is an open convex set.

AB - This paper establishes an upper bound for u-v where u is a subsolution of ut+F(u, Dxu, D2xu)=0and v is a supersolution ofvt+G(v, Dxv, D2xv)=0in (0, ∞)×Ω with Neumann boundary conditions and where Ω is an open convex set.

UR - http://www.scopus.com/inward/record.url?scp=0001657843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001657843&partnerID=8YFLogxK

U2 - 10.1006/jdeq.2000.3802

DO - 10.1006/jdeq.2000.3802

M3 - Article

AN - SCOPUS:0001657843

SN - 0022-0396

VL - 170

SP - 180

EP - 187

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this