Displaying similar documents to “Local existence and estimations for a semilinear wave equation in two dimension space”

The phase of the Daubechies filters.

Djalil Kateb, Pierre Gilles Lemarié-Rieusset (1997)

Revista Matemática Iberoamericana

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We give the first term of the asymptotic development for the phase of the N-th (minimum-phased) Daubechies filter as N goes to +∞. We obtain this result through the description of the complex zeros of the associated polynomial of degree 2N+1.

Classification of initial data for the Riccati equation

N. Chernyavskaya, L. Shuster (2002)

Bollettino dell'Unione Matematica Italiana

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We consider a Cauchy problem y ′ ⁢ x + y 2 ⁢ x = q ⁢ x , y ⁢ x x = x 0 = y 0 where x 0 , y 0 ∈ R and q ⁢ x ∈ L 1 loc ⁢ R is a non-negative function satisfying the condition: ∫ - ∞ x q ⁢ t ⁢ d ⁢ t > 0 , ∫ x ∞ q ⁢ t ⁢ d ⁢ t > 0 ⁢  for  ⁢ x ∈ R . We obtain the conditions under which y ⁢ x can be continued to all of R . This depends on x 0 , y 0 and the properties of q ⁢ x .