Local existence and uniqueness for a semi-linear accretive wave equation
نویسندگان
چکیده
We prove local existence and uniqueness of the solution (u, ut) ∈ C 0([0, T ];H1 × L2(RN )) of the semilinear wave equation utt −∆u = ut|ut| p−1 for 1 < p < 1 + 2 N .
منابع مشابه
Blow-up rate for a semi-linear accretive wave equation
X iv :0 71 0. 13 61 v3 [ m at hph ] 1 6 O ct 2 00 7 Blow-up rate for a semi-linear accretive wave equation M. Jazar∗ and Ch. Messikh Abstract. In this paper we consider the semi-linear wave equation: utt − ∆u = ut|ut| in R where 1 ≤ p ≤ 1 + 4 N−1 if N ≥ 2. We give the optimal blow-up rate for blowing up solutions of this equation. AMS Subject Classifications: 35L05,35L67
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