Differential and Integral Equations
- Differential Integral Equations
- Volume 27, Number 5/6 (2014), 425-446.
Existence and blowing up for a system of the drift-diffusion equation in $R^2$
We discuss the existence of the blow-up solution for multi-component parabolic-elliptic drift-diffusion model in two space dimensions. We show that the local existence, uniqueness and well posedness of a solution in the weighted $L^2$ spaces. Moreover, we prove that if the initial data satisfies a threshold condition, the corresponding solution blows up in a finite time. This is a system case for the blow up result of the chemotactic and drift-diffusion equation proved by Nagai  and Nagai-Senba-Suzuki  and gravitational interaction of particles by Biler-Nadzieja , . We generalize the result in Kurokiba-Ogawa  for multi-component problem and give a sufficient condition for the finite time blow up of the solution.
Differential Integral Equations, Volume 27, Number 5/6 (2014), 425-446.
First available in Project Euclid: 3 April 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 35Q60: PDEs in connection with optics and electromagnetic theory 78A35: Motion of charged particles
Kurokiba, Masaki. Existence and blowing up for a system of the drift-diffusion equation in $R^2$. Differential Integral Equations 27 (2014), no. 5/6, 425--446. https://projecteuclid.org/euclid.die/1396558090