Wave breaking for shallow water models with time decaying solutions

@article{49396,
   author = {Leite Freire, Igor},
   article_location = {San DIego (USA)},
   article_number = {4},
   doi = {http://dx.doi.org/10.1016/j.jde.2020.03.011},
   keywords = {Camassa-Holm type equations; Kato's approach; Wave breaking; Time dependent norms},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Wave breaking for shallow water models with time decaying solutions},
   url = {https://www.sciencedirect.com/science/article/pii/S0022039620301182?via%3Dihub},
   volume = {269},
   year = {2020}
}

TY  - JOUR
ID  - 49396
AU  - Leite Freire, Igor
PY  - 2020
TI  - Wave breaking for shallow water models with time decaying solutions
JF  - Journal of Differential Equations
VL  - 269
IS  - 4
SP  - 3769-3793
EP  - 3769-3793
PB  - Academic Press Inc. Elsevier Science
SN  - 00220396
KW  - Camassa-Holm type equations
KW  - Kato's approach
KW  - Wave breaking
KW  - Time dependent norms
UR  - https://www.sciencedirect.com/science/article/pii/S0022039620301182?via%3Dihub
N2  - 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.
ER  - 

LEITE FREIRE, Igor. Wave breaking for shallow water models with time decaying solutions. \textit{Journal of Differential Equations}. San DIego (USA): Academic Press Inc. Elsevier Science, 2020, roč.~269, č.~4, s.~3769-3793. ISSN~0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2020.03.011.