6 papers
An entropy approach to doubly nonlinear parabolic obstacle problems
Ruoyang Liu
This paper studies doubly nonlinear parabolic obstacle problems. We introduce a renormalized entropy formulation in which the reaction measure is encoded by evaluating the entropy…
Well-posedness and large deviations for the obstacle problem of first-order stochastic conservation laws
Ruoyang Liu, Rangrang Zhang
This paper studies the obstacle problem for first-order scalar conservation laws driven by multiplicative noise. By adapting a barrier-substitution strategy to the kinetic formulat…
Well-posedness of the obstacle problem for generalized Dean-Kawasaki equation
Ruoyang Liu, Rangrang Zhang
We investigate the obstacle problem for generalized Dean--Kawasaki equations driven by correlated conservative noise, establishing the existence, uniqueness, and -stability of…
Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation
Kai Du, Ruoyang Liu
In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conserva…
Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise
Kai Du, Ruoyang Liu, Yuxing Wang
Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative no…
The obstacle problem for stochastic porous media equations
Ruoyang Liu, Shanjian Tang
We prove the existence and uniqueness of non-negative entropy solutions of the obstacle problem for stochastic porous media equations. The core of the method is to combine the entr…