The Quenching Problem on the N-dimensional Ball
Consider the problem where β > 0 and Ω = B R (0) ≔ x ∈ IR N ; |x| < R. It is known ([AW]) that there is a positive number R o = R o (N,β) such that u exists globally if R < R o while for R> R o the solution u reaches zero in a finite time T (it quenches). The only point x o for which u(x o , t) → 0 as t 2192 T is x o = 0 (see [AK]).
KeywordsMaximum Principle Finite Time Singular Solution Positive Equilibrium Infinite Time
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