ON DECAY ESTIMATES OF SOLUTIONS
FOR SOME DEGENERATE NONLINEAR
KIRCHHOFF STRINGS WITH DISSIPATION
Kosuke Ono
Department of Mathematical Sciences
The University of Tokushima
Tokushima 770-8502, JAPAN
Abstract. We consider the initial-boundary value problem for the degenerate nonlinear dissipative wave equation of Kirchhoff type:
utt-(∫01 |ux(x,t)|2 dx)γ uxx + ut +f(u)=0,
where f(u) is like as |u|p u. If the initial energy is appropriately small and γ ≥ 1 and p>2γ, then we obtain some optimal time decay estimates of the solution u=u(t).
AMS Subject classification: 35L80, 35B40, 35L20
Keywords and phrases: dissipative wave equations, degenerate, Kirchhoff strings, decay estimates


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DOI: 10.12732/ijam.v26i3.9

Volume: 26
Issue: 3
Year: 2013