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Resumen:
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The object of this paper is the study of blowing-up phenomena for the initial-boundary value problem (Pa): ut=uxx+?eu for (x,t)?(0,1)×(0,+?), u(0,t)=asin?t and u(1,t)=0 for t?[0,+?), u(x,0)=u0(x) for x?(0,1), where u0(x) is a continuous and bounded function, and a>0, ?>0 are real constants. It is known that if the amplitude a=0 in the oscillatory boundary condition above then there exists a critical parameter ?FK (the so-called Frank-Kamenetski? parameter) such that if ??FK. The authors prove existence of a parameter ?(a,?)??FK with similar critical properties. The essential part of the paper is devoted to the study of the asymptotic behavior of ?(a,?) with respect to a and ?. For example, ?(a,?)??FK as a?0 uniformly in ?. Further, the exact dependence of ?(a,?) on the data in (Pa) is shown in the remaining limiting cases for a and ?.
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