Exponential Growth for a Fractionally Damped Wave Equation | Zendy

Mokhtar Kirane | Zendy; Nasser-edine Tatar | Zendy

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Exponential Growth for a Fractionally Damped Wave Equation

Author(s) -

Mokhtar Kirane,

Nasser-edine Tatar

Publication year - 2003

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1137

Subject(s) - mathematics , exponential function , mathematical analysis , exponential growth , fourier transform , polynomial , norm (philosophy) , nonlinear system , wave equation , physics , quantum mechanics , political science , law

Summary We consider a nonlinear wave equation with an inter nal damping represented by a fractional time, derivative and with a polynomial s ource. It is proved that the solution is unbounded and grows up exponentially in the L-p- norm for sufficiently large initial data. To this end we use some techniques based on F ourier transforms and some inequalities such as the Hardy-Littlewood inequalit y.

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