Preprints by Takayoshi Ogawa
Here is the list of available preprints (by mainly PDF file) with short discriptions.
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L^p wellposedness for the drift-diffusion system arising from the semicondunctor
device simulation
The Cauchy problem for the drift-diffusin system of the bi-polar type is treated by the mothod of the
evolution equation. By using the L^p-L^q type estimate for the
heat kernel, we show the system is time locally wellposed for the data
$L^q$ where $n/2
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Regularity condition by mean oscillation to
a weak solution of
the harmonic heat flow into sphere
This is the continuing work on the regularity criterion for the
weak solution of the 2 dimensional harmonic heat flow into a sphere.
The regularity criterion for the weak solution to the 2-dimensional
harmonic heat flow is considered. The regularity criterion by term of
the Bounded Mean Oscillation (BMO) in space and L^2 in time is
proven. This is know for the continuity properties for the strong solution.
The key method is to enploy the critical interpolation inequality in BMO of
logarithmic type and establish the monotonicity formula by mean oscillation.
This is corresponding to the monotonicity for the second derivative of the
solution in the saling point of view.
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Decay and asymptotic behavior of a solution of the Keller-Segel system
of degenerated and non-degenerated type,
This is a survey article for the global existence and finite time blow up
of the Keller-Segel system of elliptic-parabolic case.
The paper firstly summerize the result for the non-degenerated case as a reference and
show the critical threshold for the global existence and finite time
blow up for the degenarated case in terms of the power of the degeneracy of the top term.
For the crictical case, the threshold number is given by the best possible
constant of the Hardy-Littlewood-Sobolev inequality.
The decay and asymtotic profile for the decaying solution is also presented
for the subcritcal case.
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Global Existence of solutions for a nonlinearly
perturbed Elliptic Parabolic System in R^2,
Nonlinearly perturbed Keller-Segel system is considered. The system has the power
nonlinear term in the elliptic term which is considered in the literutures.
In this paper, we consider the system of simplified Keller-Segel system with
drift-heat equation with nonlinear elliptic equation.
It is known that this elliptic type of equation has at least two positive solution,
the uniquness of the solution is not expected.
Nevertheless, we show the existence and conditional uniquness of the time global
solution for the system. The key idea is to combine the variational method
to construct the time dependent system and avoid to non-uniequness problem.
Last modified, June 27, 2006.
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