Existence, uniqueness, and quenching properties of solutions for degenerate semilinear parabolic problems with second boundary conditions
In: Journal of mathematical analysis and applications, Jg. 338 (2008), Heft 2, S. 892-901
Online
academicJournal
- print, 7 ref
Let q ≥ 0, p ≥ 0, T ≤∞, D = (0, a), D = [0, a], Ω = D x (0, T), and Lu = xqut - uxx. This article considers the following degenerate semilinear parabolic initial-boundary value problem, Lu = xp f(u) in Q, u(x,0)=0 on D, ux (0, t)=0=ux(a, t) fort>0, where f(0) > 0, f' > 0, f ≥ 0, and limu→c- f(u) = 00 for some positive constant c. Existence of a unique classical solution is proved. It is shown that if p > q, then quenching occurs only at the boundary point x = a while if p < q, then the only quenching point is x = 0. If p = q, then the quenching set is D.
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Existence, uniqueness, and quenching properties of solutions for degenerate semilinear parabolic problems with second boundary conditions
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Autor/in / Beteiligte Person: | DYAKEVICH, Nadejda E |
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Zeitschrift: | Journal of mathematical analysis and applications, Jg. 338 (2008), Heft 2, S. 892-901 |
Veröffentlichung: | San Diego, CA: Elsevier, 2008 |
Medientyp: | academicJournal |
Umfang: | print, 7 ref |
ISSN: | 0022-247X (print) |
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