Error estimates for some mixed finite element methods for parabolic type problems
Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations.
Estimates for the cut-off resolvent of the Laplacian for trapping obstacles
Estimates for the maximum modulus of solutions to the Burgers system of equations.
Estimates near the boundary for solutions of second order parabolic equations.
Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain
A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.
Euler schemes and half-space approximation for the simulation of diffusion in a domain
This paper is concerned with the problem of simulation of , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain : namely, we consider the case where the boundary is killing, or where it is instantaneously reflecting in an oblique direction. Given discretization times equally spaced on the interval , we propose new discretization schemes: they are fully implementable and provide a weak error of order under some conditions. The construction...
Euler schemes and half-space approximation for the simulation of diffusion in a domain
This paper is concerned with the problem of simulation of (Xt)0≤t≤T, the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain D: namely, we consider the case where the boundary ∂D is killing, or where it is instantaneously reflecting in an oblique direction. Given N discretization times equally spaced on the interval [0,T], we propose new discretization schemes: they are fully implementable and provide a weak error of order N-1 under some conditions....
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form . We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one...
Exact null internal controllability for the heat equation on unbounded convex domains
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.
Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.
Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces...
Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.
Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.
Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker-Planck type equations.
Existence of a solution of a Fourier nonlocal quasilinear parabolic problem.
Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type
The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.
Existence of pseudo almost automorphic solutions for the heat equation with -pseudo almost automorphic coefficients.
Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities
We study the problem ∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T), in Ω, u = 0 in ∂Ω × (0,T). The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in and b(x,u₀) ∈ L¹(Ω).
Existence of solution to transpiration control problem.