Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

358

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

457-483

Kód UT WoS článku

000952317500001

EID výsledku v databázi Scopus

2-s2.0-85148664705