101 research outputs found
Global solutions to semirelativistic Hartree equations
We consider initial value problems for the semirelativistic Hartree
equations with cubic convolution nonlinearity .
Here is a sum of two Coulomb type potentials. Under a specified
decay condition and a symmetric condition for the potential we
show the global existence and scattering of solutions
Remarks on modified improved Boussinesq equations in one space dimension
We study the existence and scattering of global small amplitude
solutions to modified improved Boussinesq equations in one dimension
with nonlinear term behaving as a power as .
Solutions in space are considered for all . According to the value of , the power nonlinearity exponent
is determined. Liu \cite{liu} obtained the minimum value of
greater than at for sufficiently small Cauchy
data. In this paper, we prove that can be reduced to be greater
than at and the corresponding solution
has the time decay such as
as . We also prove nonexistence of nontrivial
asymptotically free solutions for under vanishing
condition near zero frequency on asymptotic states
On the semi-relativistic Hartree type equation
We study the global Cauchy problem and scattering problem for the semi-relativistic equation in
with nonlocal nonlinearity . We prove the existence and uniqueness of global solutions for or and the non-existence of asymptotically free solutions for . We also specify asymptotic behavior of solutions as the mass tends to zero and infinity
Sobolev inequalities with symmetry
In this paper we derive some Sobolev inequalities for radially symmetric functions in ˙H s with 1 2 < s < n 2 . We show the end point case s = 1 2 on the homogeneous Besov space ˙B 12 2;1. These results are extensions of the well-known Strauss’ inequality [11]. Also non-radial extensions are given, which show that compact embeddings are possible in some Lp spaces if a suitable angular regularity is imposed
On radial solutions of semi-relativistic Hartree equations
We consider the semi-relativistic Hartree type equation with
nonlocal nonlinearity . In \cite{chooz2}, the global well-posedness
(GWP) was shown for the value of with large data and with small
data. In this paper, we extend the previous GWP result to the case
for with radially symmetric
large data. Solutions in a weighted Sobolev space are also studied
On small amplitude solutions to the generalized Boussinesq equations
We study the existence and scattering of global small amplitude
solutions to generalized Boussinesq (Bq) and improved modified
Boussinesq (imBq) equations with nonlinear term behaving as a
power as in
ELLIPTIC ESTIMATES INDEPENDENT OF DOMAIN EXPANSION
In this paper, we consider elliptic estimates for a system with mooth variable coeffcients on a domain ½ Rn; n ¸ 2 containing the origin. e first show the invariance of the estimates under a domain expansion de¯ned y the scale that y = Rx, x; y 2 Rn with parameter R > 1, provided that the oeffcients are in a homogeneous Sobolev space. Then we apply these invariant stimates to the global existence of unique strong solutions to a parabolic ystem de¯ned on an unbounded domain
Remarks on the relativistic Hartree equations
We study the global well-posedness (GWP) and small data scattering of radial solutions of the relativistic Hartree type equations with nonlocal nonlinearity F(u) = ¸(j ¢ j¡° ¤ juj2)u, ¸ 2 R n f0g, 0 < ° < n, n ¸ 3. We establish a weighted L2 Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions
A case of human infection with Diphyllobothrium in Fukuyama City, Hiroshima Prefecture
Three strobilae with scoleces were expelled from a 16-year-old man by the administration of 600mg (20mg/kg) praziquantel. The No.1 strobila had a scolex 6.5cm in length. The No.2 strobila had a scolex 28cm in length. The No.3 strobila with a scolex and mature segments was 142cm in length. The No.3 strobila was identified as Diphyllobothrium latum by its morphological characteristics. The No.1 strobila had a scolex similar to that of the No.3 strobila. However, the No.2 strobila was equipped with a hammer-like scolex. This result suggests that the No.2 strobila belonged to species other than D. Latum
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