Related papers: Bergman-space regularity for the heat equation wit…
We consider the inhomogeneous heat equation on the half-space $\mathbb R_{+}^{d}$ with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a radius of analyticity uniform up to the boundary of the…
We consider a nonlinear stochastic heat equation on $[0,T]\times [-L,L]$, driven by a space-time white noise $W$, with a given initial condition $u_0: \mathbb{R} \to \mathbb{R}$ and three different types of (vanishing) boundary conditions:…
The Blackstock-Crighton equation models nonlinear acoustic wave propagation in thermo-viscous fluids. In the present work we investigate the associated inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain and…
Consider the semilinear heat equation $\partial_t u = \partial^2_x u + \lambda\sigma(u)\xi$ on the interval $[0\,,1]$ with Dirichlet zero boundary condition and a nice non-random initial function, where the forcing $\xi$ is space-time white…
We consider nonlinear parabolic SPDEs of the form $\partial_t u=\Delta u + \lambda \sigma(u)\dot w$ on the interval $(0, L)$, where $\dot w$ denotes space-time white noise, $\sigma$ is Lipschitz continuous. Under Dirichlet boundary…
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…
Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…
Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge is established in an $L^{2}$-setting of monomially weighted spaces. A mathematical framework is developed which…
This paper concerns the final value problem for the heat equation under the homogeneous Neumann condition on the boundary of a smooth open set in Euclidean space. The problem is here shown to be isomorphically well posed in the sense that…
Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the…
We study inhomogeneous Dirichlet boundary value problems associated to a linear parabolic equation $\frac{du}{dt}=Au$ with strongly elliptic operator $A$ on bounded and unbounded domains with white noise boundary data. Our main assumption…
We establish existence, uniqueness and higher order weighted $L_p$-Sobolev regularity for the stochastic heat equation with zero Dirichlet boundary condition on angular domains and on polygonal domains in $\mathbb{R}^2$. We use a system of…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
This is a preliminary announcement of results in the PhD. thesis of the first author concerning the nonlinear stochastic heat equation in the spatial domain $\R$, driven by space-time white noise. A central special case is the parabolic…
In this paper we study the Poisson and heat equations on bounded and unbounded domains with smooth boundary with random Dirichlet boundary conditions. The main novelty of this work is a convenient framework for the analysis of such…
We study boundary regularity for solutions to a class of equations involving the so called regional fractional Lapacians $(-\Delta)^s_\Omega $, with $\Omega\subset \mathbb{R}^N$. Recall that the regional fractional Laplacians are generated…
In this paper, we study the stochastic heat equation in the spatial domain $\mathbb{R}^d$ subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and…
We study the nonlinear steady Boltzmann equation in the half space, with phase transition and Dirichlet boundary condition. In particular, we study the regularity of the solution to the half-space problem in the situation that the gas is in…
In this paper, we consider the one-dimensional stochastic heat equation driven by a space time white noise. In two different scenarios: {\it (i)} initial condition $u_0=1$ and general nonlinear coefficient $\sigma$ and {\it (ii)}: initial…
In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The…