Wave breaking for shallow water models with time decaying solutions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F20%3AA0000086" target="_blank" >RIV/47813059:19610/20:A0000086 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039620301182?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039620301182?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2020.03.011" target="_blank" >10.1016/j.jde.2020.03.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Wave breaking for shallow water models with time decaying solutions

Popis výsledku v původním jazyce

A family of Camassa-Holm type equations with a linear term and cubic and quartic nonlinearities is considered. Local well-posedness results are established via Kato's approach. Conserved quantities for the equation are determined and from them we prove that the energy functional of the solutions is a time-dependent, monotonically decreasing function of time, and bounded from above by the Sobolev norm of the initial data under some conditions. The existence of wave breaking phenomenon is investigated and necessary conditions for its existence are obtained. In our framework the wave breaking is guaranteed, among other conditions, when the coefficient of the linear term is sufficiently small, which allows us to interpret the equation as a linear perturbation of some recent Camassa-Holm type equations considered in the literature.

Název v anglickém jazyce

Wave breaking for shallow water models with time decaying solutions

Popis výsledku anglicky

A family of Camassa-Holm type equations with a linear term and cubic and quartic nonlinearities is considered. Local well-posedness results are established via Kato's approach. Conserved quantities for the equation are determined and from them we prove that the energy functional of the solutions is a time-dependent, monotonically decreasing function of time, and bounded from above by the Sobolev norm of the initial data under some conditions. The existence of wave breaking phenomenon is investigated and necessary conditions for its existence are obtained. In our framework the wave breaking is guaranteed, among other conditions, when the coefficient of the linear term is sufficiently small, which allows us to interpret the equation as a linear perturbation of some recent Camassa-Holm type equations considered in the literature.

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

2020

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

269

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

3769-3793

Kód UT WoS článku

000534488300032

EID výsledku v databázi Scopus

2-s2.0-85081255919