Related papers: A Stefan-type stochastic moving boundary problem
We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution PDEs with constant coefficients in one space variable. The prototypical such PDE is the heat equation, for which problems of…
For characterizing the Brownian motion in a bounded domain: $\Omega$, it is well-known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; on…
In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a…
We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary,…
We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…
In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…
We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a…
While there is a long history of employing moving boundary problems in physics, in particular via Stefan problems for heat conduction accompanied by a change of phase, more recently such approaches have been adapted to study biological…
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…
We investigate the qualitative behaviour of the solutions of a stochastic boundary value problem on the half-line for a nonlinear system of parabolic reaction-diffusion equations, from a numerical point of view. The model describes the…
We consider the classic spring-mass model of running which is built upon an inverted elastic pendulum. In a natural way, there arises an interesting boundary value problem for the governing system of two nonlinear ordinary differential…
The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed…
Here, a novel 2+1-dimensional nonlinear evolution equation with temporal modulation is introduced which admits integrable Ermakov-Painlev\'e II symmetry reduction. Application is made to obtain exact solution to a class of Stefan-type…
We consider a partial differential equation that arises in the coarse-grained description of epitaxial growth processes. This is a parabolic equation whose evolution is governed by the competition between the determinant of the Hessian…
We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new…
We study a system of two reflected SPDEs which share a moving boundary. The equations describe competition at an interface and are motivated by the modelling of the limit order book in financial markets. The derivative of the moving…
This paper examines the well-posedness of the Stefan problem with a dynamic boundary condition. To show the existence of the weak solution, the original problem is approximated by a limit of an equation and dynamic boundary condition of…
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz drift coefficient and includes moment estimates for…