Odd-order quasilinear evolution equations posed on a bounded interval

Larkin, Nikolai A.; Faminskii, Andrei V.

doi:10.5269/bspm.v28i1.10816

B Soc Paran Mat

2010

DOI: 10.5269/bspm.v28i1.10816

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Odd-order quasilinear evolution equations posed on a bounded interval

Nikolai A. Larkin¹,

Andrei V. Faminskii

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Cited by 2 publications

References 29 publications

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Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation

Boukarou,

Zennir,

Bouye

et al. 2024

MATH

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By using linear, bilinear, and trilinear estimates in Bourgain-type spaces and analytic spaces, the local well-posedness of the Cauchy problem for the a Kawahara-Korteweg-de-Vries equation<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \partial_{t}u+\omega\partial_{x}^{5}u+\nu \partial_{x}^{3}u+\mu\partial_{x}u^{2}+\lambda\partial_{x}u^{3}+\mathfrak{d}(x)u = 0, $\end{document} </tex-math></disp-formula>was established for analytic initial data $ u_{0} $. Besides, based on the obtained local result, together with an analytic approximate conservation law, we prove that the global solutions exist. Furthermore, the analytic radius has a fixed positive lower bound uniformly for all time.

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Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation

Boukarou,

Zennir,

Bouye

et al. 2024

MATH

View full text Add to dashboard Cite

show abstract

Decay of Small Solutions for the Zakharov-Kuznetsov Equation posed on a half-strip

Larkin

Tronco

2011

B Soc Paran Mat

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Odd-order quasilinear evolution equations posed on a bounded interval

Cited by 2 publications

References 29 publications

Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation

Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation

Decay of Small Solutions for the Zakharov-Kuznetsov Equation posed on a half-strip

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