Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43928171" target="_blank" >RIV/49777513:23520/16:43928171 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0022039615004702" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0022039615004702</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2015.09.015" target="_blank" >10.1016/j.jde.2015.09.015</a>
Alternative languages
Result language
angličtina
Original language name
Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian
Original language description
The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator is investigated for p>2. This problem is reduced to the comparison of the trivial solution (IDENTICAL TO0, by hypothesis) with a nontrivial nonnegative solution u(x,t). The problem is closely related also to the question of uniqueness of a nonnegative solution via the weak comparison principle. In this article, realistic counterexamples to the uniqueness of a nonnegative solution, the weak comparison principle, and the strong maximum principle are constructed with a nonsmooth reaction function that satisfies neither a Lipschitz nor an Osgood standard "uniqueness" condition. Nonnegative multi-bump solutions with spatially disconnected compact supports and zero initial data are constructed between sub- and supersolutions that have supports of the same type.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN
0022-0396
e-ISSN
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Volume of the periodical
260
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
"991?1009"
UT code for WoS article
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EID of the result in the Scopus database
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