Nonexistence results for a fractional problem arising in thermal diffusion in fractal media

Nasser eddine Tatar

doi:10.1016/j.chaos.2006.08.001

Nonexistence results for a fractional problem arising in thermal diffusion in fractal media

Nasser eddine Tatar^*

^*Corresponding author for this work

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

24 Scopus citations

Abstract

We consider the Cauchy problem for the fractional differential equationD^{1 + α} u + D^β u = Δ u + h (t, x) | u |^pwith given initial data and where p > 1, -1 < α < 1, 0 < β < 2 and β < 1 + α. Nonexistence results and necessary conditions for global existence are established by means of the test-function method. These results improve and extend previous works.

Original language	English
Pages (from-to)	1205-1214
Number of pages	10
Journal	Chaos, Solitons and Fractals
Volume	36
Issue number	5
DOIs	https://doi.org/10.1016/j.chaos.2006.08.001
State	Published - Jun 2008

Bibliographical note

Funding Information:
The author is grateful to King Fahd University of Petroleum and Minerals for the facilities and the financial support it provides for research.

ASJC Scopus subject areas

Statistical and Nonlinear Physics
General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1016/j.chaos.2006.08.001

Cite this

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title = "Nonexistence results for a fractional problem arising in thermal diffusion in fractal media",

abstract = "We consider the Cauchy problem for the fractional differential equationD1 + α u + Dβ u = Δ u + h (t, x) | u |pwith given initial data and where p > 1, -1 < α < 1, 0 < β < 2 and β < 1 + α. Nonexistence results and necessary conditions for global existence are established by means of the test-function method. These results improve and extend previous works.",

author = "Tatar, \{Nasser eddine\}",

note = "Funding Information: The author is grateful to King Fahd University of Petroleum and Minerals for the facilities and the financial support it provides for research.",

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AU - Tatar, Nasser eddine

N1 - Funding Information: The author is grateful to King Fahd University of Petroleum and Minerals for the facilities and the financial support it provides for research.

PY - 2008/6

Y1 - 2008/6

N2 - We consider the Cauchy problem for the fractional differential equationD1 + α u + Dβ u = Δ u + h (t, x) | u |pwith given initial data and where p > 1, -1 < α < 1, 0 < β < 2 and β < 1 + α. Nonexistence results and necessary conditions for global existence are established by means of the test-function method. These results improve and extend previous works.

AB - We consider the Cauchy problem for the fractional differential equationD1 + α u + Dβ u = Δ u + h (t, x) | u |pwith given initial data and where p > 1, -1 < α < 1, 0 < β < 2 and β < 1 + α. Nonexistence results and necessary conditions for global existence are established by means of the test-function method. These results improve and extend previous works.

UR - https://www.scopus.com/pages/publications/38649097216

U2 - 10.1016/j.chaos.2006.08.001

DO - 10.1016/j.chaos.2006.08.001

M3 - Article

AN - SCOPUS:38649097216

SN - 0960-0779

VL - 36

SP - 1205

EP - 1214

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 5

ER -

Nonexistence results for a fractional problem arising in thermal diffusion in fractal media

Abstract

Bibliographical note

ASJC Scopus subject areas

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