| Abstract: |
| We study the impact of noise on the expected propagation in time of the boundary of the spatial support of solutions to stochastic porous-media equations with non-linear conservative noise, i.e. multiplicative noise inside a convective term.
Starting from a recent result together with M. Sauerbrey on finite speed of propagation for kinetic solutions of such equations (for which existence and non-negativity is known due to previous work of B. Fehrman and B. Gess), we formulate upper estimates on propagation rates for small times. With respect to scaling, these estimates coincide with the estimates known to be optimal in the deterministic setting. For large times, however, we observe a scaling transition in the stochastic case which gives strong indication that the presence of conservative noise terms enhances spreading significantly. For the proof, we rely on integral estimates and appropriate filtering techniques.
This is a joint work with Joshua Utley, Friedrich-Alexander University Erlangen - Nuremberg. |
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