The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.
The object of this paper is to prove existence and regularity results for non-linear elliptic differential-functional equations of the form over the functions that assume given boundary values ϕ on ∂Ω. The vector field satisfies an ellipticity condition and for a fixed x, F[u](x) denotes a non-linear functional of u. In considering the same problem, Hartman and Stampacchia [Acta Math.115 (1966) 271–310] have obtained existence results in the space of uniformly Lipschitz continuous functions...
We consider the initial value problem for an infinite system of differential-functional equations of parabolic type. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. The solutions are obtained by the monotone iterative method. We prove theorems on weak partial differential-functional inequalities as well the existence and uniqueness theorems in the class of continuous bounded functions and in the class of functions satisfying...
Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing Mikusiński’s...
Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing ...
Local existence of generalized solutions to nonlocal problems for nonlinear functional partial differential equations of first order is investigated. The proof is based on the bicharacteristics and successive approximations methods.
Existence and uniqueness of almost everywhere solutions of nonlocal problems to functional partial differential systems in diagonal form are investigated. The proof is based on the characteristics and fixed point methods.
The aim of this paper is to present a numerical approximation for quasilinear parabolic differential functional equations with initial boundary conditions of the Neumann type. The convergence result is proved for a difference scheme with the property that the difference operators approximating mixed derivatives depend on the local properties of the coefficients of the differential equation. A numerical example is given.
In this paper, we make some observations on the work of Di Fazio concerning estimates, , for solutions of elliptic equations , on a domain with Dirichlet data whenever and . We weaken the assumptions allowing real and complex non-symmetric operators and boundary. We also consider the corresponding inhomogeneous Neumann problem for which we prove the similar result. The main tool is an appropriate representation for the Green (and Neumann) function on the upper half space. We propose...