50,237 research outputs found
Some Blow-Up Problems for a Semilinear Parabolic Equation with a Potential
The blow-up rate estimate for the solution to a semilinear parabolic equation
in with 0-Dirichlet
boundary condition is obtained. As an application, it is shown that the
asymptotic behavior of blow-up time and blow-up set of the problem with
nonnegative initial data u(x,0)=M\vf (x) as goes to infinity, which have
been found in \cite{cer}, are improved under some reasonable and weaker
conditions compared with \cite{cer}.Comment: 29 page
Multiplicity Preserving Triangular Set Decomposition of Two Polynomials
In this paper, a multiplicity preserving triangular set decomposition
algorithm is proposed for a system of two polynomials. The algorithm decomposes
the variety defined by the polynomial system into unmixed components
represented by triangular sets, which may have negative multiplicities. In the
bivariate case, we give a complete algorithm to decompose the system into
multiplicity preserving triangular sets with positive multiplicities. We also
analyze the complexity of the algorithm in the bivariate case. We implement our
algorithm and show the effectiveness of the method with extensive experiments.Comment: 18 page
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