Abstract
We study the global existence, uniqueness, and asymptotic behavior of solutions to the Cauchy problem for the semilinear dissipative wave equations: (∅+∂t)u =|u|α+1 in RN × (0, ∞) with u|t=0=eu0 and ∂tu|t=0 = eu1 for a small parameter e > 0. Here, we do not assume any compactly support conditions on the initial data (u0, u1). When dimension N = 4, 5 and α is greater than a critical number 2/N which is often called Fujita's exponent, we solve the global in time solvability problem and we derive the sharp decay rates of Lp norm with p ≥ 1 of the solutions.
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