Exploration of decay estimates and global existence of solutions in nonlinear dissipative wave equations, indicating significant results for mathematical applications.
First we shall derive the basic decay estimates of the total energy and L 2 -norm of a solution to the mixed problem for the linear dissipative wave equation in an exterior domain with the initial data satisfying some further restrictions as lxl --+ +oo.That decay estimates are faster than the usual one.Second we shall apply the decay estimates above to the exterior mixed problem of the semilinear dissipative wave equation in an exterior domain and we shall derive the small data global existence property to that problem with the power satisfying 1 + 4/ (N + 2) < p~N/(N-2) (N=3,4,5) on the nonlinear term jujP.
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Ryo Ikehata (2002) studied this question.
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