Nonexistence of Global Solutions and Bifurcation Analysis for a Boundary-Value Problem of Parabolic Type

Abstract

Abstract. The aim of this paper is to present a bifurcation analysis on the existence of the nonexistence of a global solution for a semilinear parabolic equation and to characterize the local stability and the instability of the corresponding steady-state solutions. The bifurcation result can be described either by a parameter X for a fixed spatial domain Ü or by varying Í2 for a fixed A. The stability analysis gives a result which can be used to determine the stability or instability problem when the system possesses nonintersecting multiple steady-state solutions.

On the explosion of chain-thermal reactions

“…It is trivial to prove that u(t) -* 00 as / -»"7r(2Xb)' ]/2 . We claim that u{t) is indeed a lower bound for z 0 , but we see no point in finding an upper solution in this analysis (which actually exists) since the method of approach is clearly written in [9]. What we have now is that *"(/)> Xsec 2 ((XV2) 1/2 0 (3.4) and ( where h 2 = Xb -((e -a -2)/2) 2 .…”

A nonlinearity lagging for the solution of nonlinear steady state reaction diffusion problems

“…and a = 2ρ/c. Now, as observed in [21], if there exists an integer ν 0 such that γ < 1 for all ν ≥ ν 0 , we can write (28) as…”

“…then, at the left hand side of inequality (27) we have to add the term α min u * − u (ν+1) 2 h and in (28) the parameter γ becomes…”

Monotone methods for semilinear parabolic and elliptic equations on graphs

“…As a method to study the characterizes of solutions, the upper and lower approach has been attracted much attention from a lot of researchers for many years, see [3,16,26,27,28] and references therein. Motivated by one of those papers, which establish the monotone methods in nonlinear elliptic and parabolic boundary value problems [27].…”