For intersection and union, we show an exponential simulation, and prove that the exponential blow-up cannot be avoided.
Moreover, the computation of the transitive closure is investigated and it is proved that there can be an exponential blow-up from input to output size.
However, this does not restrict the maximal edit distance of matches in contrast to trie-based methods which avoid exponential blow-up with such restrictions.
This classical CSP optimization is enough to avoid most of the trivial exponential blow-ups and corresponds to the initial phase of parallel places detection and merging of the equality classes optimization [ 21] for the standard Fourier-Motzkin algorithm.
When the fractional order damped and sources term are the terms of the wave equation, Kirane and Tatar [11] and Tatar [12] proved that exponential growth and blow-up result for sufficient large initial data.
Finally, we obtain existence result of global solutions with exponential decay and show the blow-up in finite time of solutions.
In this paper, we study the blow-up solutions, global existence, and exponential decay estimates for a class of second order parabolic problems with Dirichlet boundary conditions.
Many authors have studied the blow-up solutions, global existence, and exponential decay estimates of nonlinear parabolic problems (see, for instance, [1 14]).
These results are existence counterparts of one by Druet in [O. Druet, Multibump analysis in dimension 2: Quantification of blow-up levels, Duke Math. J. 132 (2) (2006) 217–269] which classifies asymptotic bounded energy levels of blow-up solutions for a class of nonlinearities of critical exponential growth, including this one as a prototype case.
In this short paper I prove a Harnack type inequality of the blowing-up solutions for a class of fourth-order equations with exponential growth on a compact four manifold.
