Related papers: Strong maximum principle for radiative tranfer typ…
We consider solving a generalized Allen-Cahn equation coupled with a passive convection for a given incompressible velocity field. The numerical scheme consists of the first order accurate stabilized implicit explicit time discretization…
The maximum principle for SPDEs is established in multidimensional $C^{1}$ domains. An application is given to proving the H\"older continuity up to the boundary of solutions of one-dimensional SPDEs.
We provide a proof of strong maximum and minimum principles for fully nonlinear uniformly parabolic equations of second order. The approach is of parabolic nature, slightly differs from the earlier one proposed by L. Nirenberg and does not…
In the work of Navier-Stokes (NSE) equation, derived a nonlinear parabolic equation for kinetic energy density, and identified an important property of this equation - the maximum principle. The latter shows the validity of the maximum…
The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the…
We obtain the comparison principle for discontinuous viscosity sub- and supersolutions of nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The nonlocal terms are integro-differential operators in L\'evy…
This article establishes a discrete maximum principle (DMP) for the approximate solution of convection-diffusion-reaction problems obtained from the weak Galerkin finite element method on nonuniform rectangular partitions. The DMP analysis…
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first establish a stochastic maximum principle (SMP) as a necessary…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
Through the Maximum principle we define the principal eigenvalue for a class of fully-nonlinear operators that are the non-variational equivalent of the p-Laplacian. We also obtain some a priori Holder estimates for non-negative solutions…
We are interested in some properties related to the solutions of non-local diffusion equations with divergence free drift. Existence, maximum principle and a positivity principle are proved. In order to study Holder regularity, we apply a…
In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of…
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) in [9] and the dynamic programming principle (DPP) in [10] for a fully coupled forward-backward stochastic controlled system (FBSCS)…
In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first…
Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple…
We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of $\mathbb{R}^n$. The simplicity and robustness of our maximum principle-based argument provides for its…