DSpace Collection:

Dispersive Estimate for the Wave Equation with Short-Range Potential

2011-07-20T08:03:08Z

Title: Dispersive Estimate for the Wave Equation with Short-Range Potential Authors: Visciglia, Nicola Abstract: In this paper we consider a potential type perturbation of the three dimensional wave equation: $\Box u + V(x)u = 0 u(x, 0) = 0, \partial_t u(x, 0) = f$, where the potential $V \geq 0$ satisfies the following decay assumption: $|V (x)| \leq \frac{C}{1+|x|^{2+\epsilon_0}}$, for some C, $\epsilon_0 > 0$. We establish some dispersive estimates for the associated propagator. Type: Articolo

Blow-up for Semilinear Wave Equations with a Data of the Critical Decay having a Small Loss

2011-03-30T23:34:58Z

Title: Blow-up for Semilinear Wave Equations with a Data of the Critical Decay having a Small Loss Authors: Kurokawa, Yuki; Takamura, Hiroyuki Abstract: It is known that we have a global existence for wave equations with super-critical nonlinearities when the data has a critical decay of powers. In this paper, we will see that a blow-up result can be established if the data decays like the critical power with a small loss such as any logarithmic power. This means that there is no relation between the critical decay of the initial data and the integrability of the weight, while the critical power of the nonlinearity is closely related to the integrability. The critical decay of the initial data is determined only by scaling invariance of the equation. We also discuss a nonexistence of local in time solutions for the initial data increasing at infinity. Type: Articolo

Concentration of Local Energy for Two-dimensional Wave Maps

2011-07-20T08:10:25Z

Title: Concentration of Local Energy for Two-dimensional Wave Maps Authors: Georgiev, Vladimir; Ivanov, Angel Abstract: We construct some particular kind of solution to the two - dimensional equivariant wave map problem with inhomogeneous source term in space-time domain of type $\Omega_\alpha(t) = {x \in \mathbb R^2 : |x|^\alpha < t}$, where $\alpha\in (0, 1]$. More precisely, we take the initial data $(u_0, u_1)$ at time T in the space $H^{1+\epsilon} \times H^\epsilon$ with some $\epsilon > 0$. The source term is in $L^1((0, T); H^\epsilon(\Omega_\alpha(t)))$ and we show that the $H^{1+\epsilon}$ -norm of the solution blows-up, when $t \rightarrow 0_+$ and $\alpha\in (0, 1 − \epsilon)$. Type: Articolo

Isomorphism of Commutative Group Algebras over all Fields

2011-03-30T23:34:49Z

Title: Isomorphism of Commutative Group Algebras over all Fields Authors: Danchev, Peter V. Abstract: It is argued that the commutative group algebra over each field determines up to an isomorphism its group basis for any of the following group classes: • Direct sums of cocyclic groups • Splitting countable modulo torsion groups whose torsion parts are direct sums of cyclics; • Splitting groups whose torsion parts are separable countable • Groups whose torsion parts are algebraically compact • Algebraically compact groups These give a partial positive answer to the R.Brauer’s classical problem. Type: Articolo