相关论文: Support theorem for a singular semilinear stochast…

We extend the invariant manifold method for analyzing the asymptotics of dissipative partial differential equations on unbounded spatial domains to treat equations in which the linear part has order greater than two. One important example…

We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of…

This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…

We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear…

We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…

These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute, Imperial College London, and EPFL. It is an attempt to give a reasonably self-contained presentation of…

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and…

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing…

We investigate a class of parametric elliptic semilinear partial differential equations of second order with homogeneous essential boundary conditions, where the coefficients and the right-hand side (and hence the solution) may depend on a…

We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing…

We consider semilinear stochastic evolution equations on Hilbert spaces with multiplicative Wiener noise and linear drift term of the type $A + \varepsilon G$, with $A$ and $G$ maximal monotone operators and $\varepsilon$ a "small"…

We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show that for a mixture of spherical Gaussian $P$ (sGMM) in a…

We provide a necessary and sufficient condition for the representability of a function as the classical multidimensional Laplace transform, when the support of the representing measure is contained in some generalized semi-algebraic set.…

A class of stochastic parabolic equations with singular potentials is analysed in the chaos expansion setting where the Wick product is used to give sense to the product of generalized stochastic processes. For the analysis of such…

A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…

By studying parabolic equations in mixed-norm spaces, we prove the existence and uniqueness of strong solutions to stochastic differential equations driven by Brownian motion with coefficients in spaces with mixed-norm, which extends Krylov…

In this paper, we establish a sharp $C^{2+\alpha}$-theory for stochastic partial differential equations of parabolic type in the whole space.