ISSN:
0170-4214
Schlagwort(e):
Engineering
;
Numerical Methods and Modeling
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Mathematik
Notizen:
In this paper we study the following problem:ut-Δu=-f(u) in Ω×(0, T)≡QT,∂u ∂n=g(u) on ∂Ω×(0, T)≡ST,u(x, 0)=u0(x) in Ω, where Ω⊂∝N is a smooth bounded domain, f and g are smooth functions which are positive when the argument is positive, and u0(x)〉0 satisfies some smooth and compatibility conditions to guarantee the classical solution u(x, t) exists. We first obtain some existence and non-existence results for the corresponding elliptic problems. Then, we establish certain conditions for a finite time blow-up and global boundedness of the solutions of the time-dependent problem. Further, we analyse systems with same kind of boundary conditions and find some blow-up results. In the last section, we study the corresponding elliptic problems in one-dimensional domain. Our main method is the comparison principle and the construction of special forms of upper-lower solutions using related equations. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.
Materialart:
Digitale Medien
