Critical exponents for semilinear dissipative wave equations in RN

We shall present new critical exponents 1 + 2m/N with m ∈ [1, 2] to the Cauchy problem ut t −Δu+ut = |u|p−1u with the initial data [u0,u1] ∈ (H1(RN)∩Lm(RN))× (L2(RN) ∩ Lm(RN)); that is, the small data global existence property can be derived to the Cauchy problem above with power 1 + 2m/N < p < +∞ (N = 1, 2). Furthermore, the small data global nonexistence of solutions will be discussed in the case when 1