Multi-dimensional explosion due to a concentrated nonlinear source
نویسندگان
چکیده
منابع مشابه
A Blow-up Criterion for a Degenerate Parabolic Problem Due to a Concentrated Nonlinear Source
Let q, a, b, and T be real numbers with q ≥ 0, a > 0, 0 < b < 1, and T > 0. This article studies the following degenerate semilinear parabolic first initial-boundary value problem, xut(x, t)− uxx(x, t) = aδ(x− b)f (u(x, t)) for 0 < x < 1, 0 < t ≤ T, u(x, 0) = ψ(x) for 0 ≤ x ≤ 1, u(0, t) = u(1, t) = 0 for 0 < t ≤ T, where δ (x) is the Dirac delta function, and f and ψ are given functions. It is ...
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A criterion for the quenching of the solution for a degenerate semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source situated at b is given. The locations of b for global existence of the solution and for the quenching of the solution are given. AMS (MOS) Subject Classification. 35K60, 35K57, 35K65, 35B35
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.03.029