相关论文: Scalar Conservation Laws with white noise initial …
We show that perturbing ill-posed differential equations with (potentially very) smooth random processes can restore well-posedness -- even if the perturbation is (potentially much) more regular than the drift component of the solution. The…
We prove the exponential stability of the zero solution of a stochastic differential equation with a H\"older noise, under the strong dissipativity assumption. As a result, we also prove that there exists a random pullback attractor for a…
In this article, we consider the following stochastic fractional diffusion equation \begin{equation*} \left(\partial^{\beta}+\dfrac{\nu}{2}\left(-\Delta\right)^{\alpha / 2}\right) u(t, x)= \lambda\: I_{0_+}^{\gamma}\left[u(t, x) \dot{W}(t,…
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…
Building on the information-theoretic perspective of P.~D.~Lax [\textit{Proc.\ Sympos., Math.\ Res.\ Center, Univ.\ Wisconsin}, 1978], we establish a two-sided quantitative compactness estimate for numerical solutions of scalar conservation…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
A classic method for computing the mass function of dark matter halos is provided by excursion set theory, where density perturbations evolve stochastically with the smoothing scale, and the problem of computing the probability of halo…
In this article, we identify the necessary and sufficient conditions for the existence of a random field solution for some linear s.p.d.e.'s of parabolic and hyperbolic type. These equations rely on a spatial operator $\cL$ given by the…
The skew Brownian motion is a strong Markov process which behaves like a Brownian motion until hitting zero and exhibits an asymmetry at zero. We address the following question: what is a natural counterpart of the skew Brownian motion in…
We investigate $L^2$-contraction and time-asymptotic stability of large shock for scalar viscous conservation laws with polynomial flux. For the strictly convex flux $f(u)=u^p $ with $2\leq p \leq 4$, we can prove $L^2$-contraction and…
We introduce a shell (``GOY'') model for turbulent binary fluids. The variation in the concentration between the two fluids acts as an active scalar leading to a redefined conservation law for the energy, which is incorporated into the…
We unravel the linear stability properties of an otherwise stagnant ultrathin non-wetting liquid film of thickness $h_o$ coating a spherical substrate of radius $R$. The configuration is known to be unstable due to the competition of the…
This paper provides an extended case study of the cutoff phenomenon for a prototypical class of nonlinear Langevin systems with a single stable state perturbed by an additive pure jump L\'evy noise of small amplitude $\varepsilon>0$, where…
In excursion set theory the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed…
We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy…
We consider a p-system of conservation laws that emerges in one dimensional elasticity theory. Such system is determined by a function $W$, called strain-energy function. We consider four forms of $W$ which are known in the literature.…
Consider the hyperbolic nonlinear Schr\"odinger equation (HNLS) over $\mathbb{R}^d$ $$ iu_t + u_{xx} - \Delta_{\textbf{y}} u + \lambda |u|^\sigma u=0. $$ We deduce the conservation laws associated with (HNLS) and observe the lack of…
We study a nonlocal regularisation of a scalar conservation law given by a fractional derivative of order between one and two. The nonlocal operator is of Riesz-Feller type with skewness two minus its order. This equation describes the…
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time…
Using a matched asymptotic expansion we analyze the two-dimensional, near- critical reflection of a weakly nonlinear, internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the…