On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification.
On the well-posedness of the heat equation on unbounded domains.
On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations.
On viscosity solutions for nontotally parabolic fully nonlinear equations
Opposing flows in a one dimensional convection-diffusion problem
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...
Optimal boundary control for a time dependent thermistor problem.
Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels
We consider a distributed system in which the state q is governed by a parabolic equation and a pair of controls v = (h,k) where h and k play two different roles: the control k is of controllability type while h expresses that the state q does not move too far from a given state. Therefore, it is natural to introduce the control point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method...
Optimal control of a stochastic heat equation with boundary-noise and boundary-control
We are concerned with the optimal control of a nonlinear stochastic heat equation on a bounded real interval with Neumann boundary conditions. The specificity here is that both the control and the noise act on the boundary. We start by reformulating the state equation as an infinite dimensional stochastic evolution equation. The first main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The C1 regularity...
Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations
We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order in the -norm if the method uses polynomials of order . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order . Further we consider a residual-based a posteriori...
Optimal regularity for mixed parabolic problems in spaces of functions which are Hölder continuous with respect to space variables
Oscillation of a logistic equation with delay and diffusion
This paper establishes oscillation theorems for a class of functional parabolic equations which arises from logistic population models with delays and diffusion.
Overimplicit methods for the solution of evolution problems
Parabolic boundary-value problems with equivalued surface on the domain with a thin layer.
Parabolic Differential Equations and Inequalities with Several Time Variables.
Parabolic equations with multiple singularities
Parabolic equations with robin type boundary conditions in a non-rectangular domain.
Parabolic equations with VMO coefficients in Morrey spaces.
Parabolic initial-boundary value problems in Orlicz spaces
We prove some time mollification properties and imbedding results in inhomogeneous Orlicz-Sobolev spaces which allow us to solve a second order parabolic equation in Orlicz spaces.
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space [...] W˙2,1p,φ(Q,ω).
Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation.