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ON LARGE-TIME DECAY OF SOLUTIONS TO AN INITIAL-BOUNDARY VALUE PROBLEM ON A SEMI-AXIS FOR THE GENERALIZED KAWAHARA EQUATION

Annotation

An initial-boundary value problem on a semi-axis for the generalized Kawahara equation with an absorption term which can degenerate on a bounded interval is considered. A result on large-time decay of weak solutions is established.

Keywords

Kawahara equation; initial-boundary value problem; large-time decay of solutions

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UDC

517.958

Pages

1331-1337

References

1. Kawahara T. Oscillatory solitary waves in dispersive media // J. Phys. Soc. Japan. 1972. V. 33. № 1. P. 260–264. 2. Linares F., Pazoto A.F. Asymptotic behavior of the Korteweg–de Vries equation posed in a quarter plane // J. Differential Equ. 2009. V. 246. P. 1342–1353. 3. Pazoto A.F., Rosier R. Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line // Descrete Contin. Dyn. Syst., Ser B. 2010. V. 14. P. 1511–1535. 4. Cavalcanti M.M., Domingos Cavalcanti V.N., Faminskii A., Natali F. Decay of solutions to damped Korteweg–de Vries equation // Appl. Math. Optim. 2012. V. 65. № 2. P. 221–251. 5. Sangare K., Faminskij A.V. Slabye reshenija smeshannoj zadachi v polupolose dlja obobshhennogo uravnenija Kavahary // Matem. zametki. 2009. T. 85. № 1. S. 98–109. 6. Opritova M.A., Faminskij A.V. O nachal'no-kraevoj zadache v polupolose dlja obobshhennogo uravnenija Kavahary // Ukr. matem. vestnik. 2014. T. 11. № 3. S. 312–339. 7. Kuvshinov R.V., Faminskij A.V. Smeshannaja zadacha v polupolose dlja uravnenija Kavahary // Diff. uravnenija. 2009. T. 45. № 3. S. 391–402. 8. Shananin N.A. O chastichnoj kvazianalitichnosti obobshhennyh reshenij slabo nelinejnyh differencial'nyh uravnenij so vzveshennymi proizvodnymi // Matem. zametki. 2000. T. 68. № 4. S. 608–619.

Received

2015-06-11

Section of issue

Scientific articles

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