PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION

Blanchard P, Röckner M, Russo F (2010)
ANNALS OF PROBABILITY 38(5): 1870-1900.

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We consider a porous media type equation over all of R-d, d = 1, with monotone discontinuous coefficient with linear growth, and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. The interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. One of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of a linear PDE on R-1 with not necessarily continuous coefficients.
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Blanchard P, Röckner M, Russo F. PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION. ANNALS OF PROBABILITY. 2010;38(5):1870-1900.
Blanchard, P., Röckner, M., & Russo, F. (2010). PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION. ANNALS OF PROBABILITY, 38(5), 1870-1900.
Blanchard, P., Röckner, M., and Russo, F. (2010). PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION. ANNALS OF PROBABILITY 38, 1870-1900.
Blanchard, P., Röckner, M., & Russo, F., 2010. PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION. ANNALS OF PROBABILITY, 38(5), p 1870-1900.
P. Blanchard, M. Röckner, and F. Russo, “PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION”, ANNALS OF PROBABILITY, vol. 38, 2010, pp. 1870-1900.
Blanchard, P., Röckner, M., Russo, F.: PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION. ANNALS OF PROBABILITY. 38, 1870-1900 (2010).
Blanchard, Philippe, Röckner, Michael, and Russo, Francesco. “PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF AN IRREGULAR POROUS MEDIA TYPE EQUATION”. ANNALS OF PROBABILITY 38.5 (2010): 1870-1900.
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