Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems

Hendrik J. Kuiper

Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems

Hendrik J. Kuiper

Mathematical and Statistical Sciences, School of (SoMSS)

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

15 Scopus citations

Abstract

We consider the problem (formula presented) with nonnegative, nontrivial, continuous initial condition, (formula presented) An integral inequality is obtained that can be used to find an exponent p_c such that this problem has no nontrivial global solution when p ≤ p_c. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu₀(x), σ > 0, by obtaining a bound of the form T ≤ C₀σ^-θ.

Original language	English (US)
Pages (from-to)	1-11
Number of pages	11
Journal	Electronic Journal of Differential Equations
Volume	2003
State	Published - Jun 13 2003

Keywords

Blow-up
Critical exponent
Lifespan
Nonlinear parabolic equation

ASJC Scopus subject areas

Analysis

Cite this

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title = "Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems",

abstract = "We consider the problem (formula presented) with nonnegative, nontrivial, continuous initial condition, (formula presented) An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p ≤ pc. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu0(x), σ > 0, by obtaining a bound of the form T ≤ C0σ-θ.",

keywords = "Blow-up, Critical exponent, Lifespan, Nonlinear parabolic equation",

author = "Kuiper, \{Hendrik J.\}",

year = "2003",

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day = "13",

language = "English (US)",

volume = "2003",

pages = "1--11",

journal = "Electronic Journal of Differential Equations",

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publisher = "Texas State University - San Marcos",

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TY - JOUR

T1 - Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems

AU - Kuiper, Hendrik J.

PY - 2003/6/13

Y1 - 2003/6/13

N2 - We consider the problem (formula presented) with nonnegative, nontrivial, continuous initial condition, (formula presented) An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p ≤ pc. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu0(x), σ > 0, by obtaining a bound of the form T ≤ C0σ-θ.

AB - We consider the problem (formula presented) with nonnegative, nontrivial, continuous initial condition, (formula presented) An integral inequality is obtained that can be used to find an exponent pc such that this problem has no nontrivial global solution when p ≤ pc. This integral inequality may also be used to estimate the maximal T > 0 such that there is a solution for 0 ≤ t < T. This is illustrated for the case ρ ≡ 1 and h ≡ 1 with initial condition u(x, 0) = σu0(x), σ > 0, by obtaining a bound of the form T ≤ C0σ-θ.

KW - Blow-up

KW - Critical exponent

KW - Lifespan

KW - Nonlinear parabolic equation

UR - https://www.scopus.com/pages/publications/3042582256

UR - https://www.scopus.com/pages/publications/3042582256#tab=citedBy

M3 - Article

AN - SCOPUS:3042582256

SN - 1072-6691

VL - 2003

SP - 1

EP - 11

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Life span of nonnegative solutions to certain quasilinear parabolic cauchy problems

Abstract

Keywords

ASJC Scopus subject areas

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