Related papers: Stochastic Generalized Porous Media Equations with…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
This paper investigates a class of generalized mean-reflected McKean-Vlasov type backward stochastic differential equations (BSDEs). Our new framework combines a mean reflection constraint on the solution's expectation with a generalized…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients…
The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009).…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which…
We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion…
We show that locally bounded, local weak solutions to certain nonlocal, nonlinear diffusion equations modeled on the fractional porous media and fast diffusion equations given by \begin{align*} \partial_t u + (-\Delta)^s(|u|^{m-1}u) = 0…
For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…
Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous…
This work extends Perron's method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.
This article studies the homogenization of hyperbolic-parabolic equations in porous media with tiny holes. We assume that the holes are periodically distributed and that the coefficients of the equations are periodic. Using the multi-scale…
We analyze the time reversal of waves in a turbulent medium using the parabolic Markovian model. We prove that the time reversal resolution can be a nonlinear function of the wavelength and independent of the aperture. We establish a…
Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that…
In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…
Unique existence of solutions to porous media equations driven by continuous linear multiplicative space-time rough signals is proven for initial data in $L^1(\mathcal {O})$ on bounded domains $\mathcal {O}$. The generation of a continuous,…
We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We…
In this paper, we study the stochastic-periodic homogenization of Non-stationary Navier-Stokes Type Equations on anisotropic heterogeneous media. More precisely, we are interested in the stochastic-periodic homogenization of its variational…