Gradient flows of non convex functionals in Hilbert spaces and applications
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Growth of semigroups in discrete and continuous time
We show that the growth rates of solutions of the abstract differential equations ẋ(t) = Ax(t), , and the difference equation are closely related. Assuming that A generates an exponentially stable semigroup, we show that on a general Banach space the lowest growth rate of the semigroup is O(∜t), and for it is O(∜n). The similarity in growth holds for all Banach spaces. In particular, for Hilbert spaces the best estimates are O(log(t)) and O(log(n)), respectively. Furthermore, we give conditions...
High regularity of the solution of a nonlinear parabolic boundary-value problem.
High-degree precision decomposition method for an evolution problem.
Higher order singular perturbation method for linear differential equations in Banach spaces
Hille-Yosida theory in convenient analysis.
A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some applications to the theory of infinite dimensional heat equations are given.
Hölder regularity in non autonomous degenerate abstract parabolic equations
Homogenization of linear and nonlinear ordinary differential equations with time depending coefficients
Hopf bifurcation for fully nonlinear equations in Banach space
Hyperbolic differential-operator equations on a whole axis.
Identification problems for degenerate parabolic equations
This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different...
Implicit Differential Equation In Locally Convex Spaces
Impulsive fractional differential equations in Banach spaces.
Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.
Impulsive semilinear neutral functional differential inclusions with multivalued jumps
In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.
Inertial manifolds for nonautonomous dynamical systems and for nonautonomous evolution equations
Inhomogeneous linear differential equations in Banach spaces
Initial boundary value problems for second order impulsive functional differential inclusions.
Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach
This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference...
Integral manifold of the parabolic differential equation with deviating argument