J
2020
Wave breaking for shallow water models with time decaying solutions
LEITE FREIRE, Igor
Basic information
Original name
Wave breaking for shallow water models with time decaying solutions
Authors
LEITE FREIRE, Igor (76 Brazil, guarantor, belonging to the institution)
Edition
Journal of Differential Equations, San DIego (USA), Academic Press Inc. Elsevier Science, 2020, 0022-0396
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/20:A0000086
Organization unit
Mathematical Institute in Opava
Keywords in English
Camassa-Holm type equations; Kato's approach; Wave breaking; Time dependent norms
Tags
International impact, Reviewed
V originále
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.
Displayed: 24/12/2024 13:41