DSpace Collection:
http://hdl.handle.net/10077/4157
Sun, 29 Jan 2023 20:04:19 GMT2023-01-29T20:04:19ZDispersive Estimate for the Wave Equation with Short-Range Potential
http://hdl.handle.net/10077/4195
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.Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10077/41952003-01-01T00:00:00ZBlow-up for Semilinear Wave Equations with a Data of the Critical Decay having a Small Loss
http://hdl.handle.net/10077/4194
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.Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10077/41942003-01-01T00:00:00ZConcentration of Local Energy for Two-dimensional Wave Maps
http://hdl.handle.net/10077/4193
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 $\alpha\in (0, 1 − \epsilon)$.Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10077/41932003-01-01T00:00:00ZIsomorphism of Commutative Group Algebras over all Fields
http://hdl.handle.net/10077/4192
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.Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10077/41922003-01-01T00:00:00Z