Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F23%3AA0000196" target="_blank" >RIV/47813059:19610/23:A0000196 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022039623000803" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039623000803</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2023.02.011" target="_blank" >10.1016/j.jde.2023.02.011</a>
Alternative languages
Result language
angličtina
Original language name
Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations
Original language description
We study formation of singularities and persistence properties of solutions for a class of non-local and non-linear evolution equations with an arbitrary function and a non-negative (dissipation) parameter, which includes the famous Camassa-Holm equation and other recently reported hydrodynamic models as particular members. In case such a parameter is positive, solutions emanating from Cauchy problems have time decaying norms bounded from above by the norm of the corresponding initial datum. Whenever the function is even, for a given odd initial datum with slope satisfying a certain relation involving the dissipation parameter, then the corresponding solution of the problem breaks at finite time. We can also describe scenarios for the occurrence of wave breaking for more general initial data or functions, provided that those latter satisfy certain conditions on their first derivatives. We also study asymptotic behavior and unique continuation properties for solutions of the equation.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
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
1090-2732
Volume of the periodical
358
Issue of the periodical within the volume
June
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
457-483
UT code for WoS article
000952317500001
EID of the result in the Scopus database
2-s2.0-85148664705