相关论文: On a vector-valued generalisation of viscosity sol…

In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and also for the level set mean curvature flow, which is an example of singular degenerate…

Systems of the first order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of solutions involve in many cases product of distributions. In this paper we study such a…

A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of…

We consider the problem of computing the integrable sub-distributions of the non-integrable Vessiot distribution of multi-dimensional second order partial differential equations (PDEs). We use Vessiot theory and solvable structures to find…

In this paper we prove existence and uniqueness of viscosity solutions of elliptic systems associated to fully nonlinear operators for minimization problems that involve interconnected obstacles. This system appears, among other, in the…

In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…

We provide a representation formula for viscosity solutions to an elliptic Dirichlet problem involving Pucci's extremal operators. This is done through a dynamic programming principle derived from Denis, Hu and Peng (2010). The formula can…

The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between…

This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward…

We directly apply the theory of viscosity solutions to partial differential equations of order greater than two. We prove that there exists a solution in $C^{2,\alpha}(B_R)\cap C(\overline{B_R})$ for the inhomogeneous $\infty$-Bilaplacian…

This paper proves the existence of viscosity solutions of path dependent semilinear PDEs via Perron's method, i.e. via showing that the supremum of viscosity subsolutions is a viscosity solution. We use the notion of viscosity solutions…

In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under the certain conditions imposed on the sequence of parameters, strong convergence theorem is…

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version…

We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…

We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…

We present a novel variational derivation of the Maxwell-GLM system, which augments the original vacuum Maxwell equations via a generalized Lagrangian multiplier approach (GLM) by adding two supplementary acoustic subsystems and which was…

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…

We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of…

Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…

Inferring continuum models directly from video is hampered by two facts: the recorded field is uncalibrated image intensity rather than a physical state, and direct numerical differentiation of noisy frames is unstable. We develop a…