Abstrakt
The present work deals with stochastic porous media equation with multiplicative noise, driven by fractional Brownian motion B-(H) with Hurst index H > 1/2. The stochastic integral with integrator B-(H) is defined pathwise following the theory developed by Zahle [24], based on the so-called fractional derivatives.
It is shown that there is a one-to-one correspondence between solutions to the stochastic equation and solutions to its deterministic counterpart. By means of this correspondence and exploiting properties of the deterministic porous media equation, the existence, uniqueness, regularity and long-time properties of the solution is established.
We also prove that the solution forms a random dynamical system in an appropriate function space.