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In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary.
A class of Markov processes associated with nonlinear parabolic equations
McKean, H. P. (1966) · 1911
Earlier work this paper cites.
Foundations of kinetic theory
Kac, M. (1956) · 1956
Earlier work this paper cites.
Equations of Mathematical Physics
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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