Finite Time Blow up for Critical Wave Equations in High Dimensions: Completion of the Proof of Strauss Conjecture
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چکیده
We prove that solutions to the critical wave equation (1.1) with dimension n ≥ 4 can not be global if the initial values are positive somewhere and nonnegative. This completes the solution to the famous conjecture about semilinear wave equations of the form ∆u− ∂ t u + |u| = 0. The rest of the cases, the lower dimensional case n ≤ 3, and the sub or super critical cases were settled many years earlier by the work of several authors.
منابع مشابه
Finite Time Blow up for Critical Wave Equations in High Dimensions
The number pc(n) is known as the critical exponent of problem (1.1), since it divides (1, ∞) into two subintervals so that the following take place: If p ∈ (1, pc(n)), then solutions with nonnegative initial values blow up in finite time; if p ∈ (pc(n), ∞), then solutions with small (and sufficiently regular) initial values exist for all time (see [St] e.g.). The proof has an interesting and ex...
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تاریخ انتشار 2005