Displaying similar documents to “Forced periodic vibrations of an elastic system with elastico-plastic damping”

Cauchy problem for the complex Ginzburg-Landau type Equation with L p -initial data

Daisuke Shimotsuma, Tomomi Yokota, Kentarou Yoshii (2014)

Mathematica Bohemica

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This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation u t - ( λ + i α ) Δ u + ( κ + i β ) | u | q - 1 u - γ u = 0 in N × ( 0 , ) with L p -initial data u 0 in the subcritical case ( 1 q < 1 + 2 p / N ), where u is a complex-valued unknown function, α , β , γ , κ , λ > 0 , p > 1 , i = - 1 and N . The proof is based on the L p - L q estimates of the linear semigroup { exp ( t ( λ + i α ) Δ ) } and usual fixed-point argument.

On the H p - L q boundedness of some fractional integral operators

Pablo Rocha, Marta Urciuolo (2012)

Czechoslovak Mathematical Journal

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Let A 1 , , A m be n × n real matrices such that for each 1 i m , A i is invertible and A i - A j is invertible for i j . In this paper we study integral operators of the form T f ( x ) = k 1 ( x - A 1 y ) k 2 ( x - A 2 y ) k m ( x - A m y ) f ( y ) d y , k i ( y ) = j 2 j n / q i ϕ i , j ( 2 j y ) , 1 q i < , 1 / q 1 + 1 / q 2 + + 1 / q m = 1 - r , 0 r < 1 , and ϕ i , j satisfying suitable regularity conditions. We obtain the boundedness of T : H p ( n ) L q ( n ) for 0 < p < 1 / r and 1 / q = 1 / p - r . We also show that we can not expect the H p - H q boundedness of this kind of operators.