Convergence in evolutionary variational inequalities with hysteresis nonlinearities
Convergence results for nonlinear evolution inclusions
In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for the multivalued...
Convexity of the orientor field and the solution set of a class of evolution inclusions
Correction to our paper “Periodic solutions to abstract differential equations”
Cross-sections of solution funnels in Banach spaces
Degenerate and Singular Evolution Equations in Banach Space.
Deterministic homogenization of parabolic monotone operators with time dependent coefficients.
Differential Equations in Abstract Cones
We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinear
Differential equations in banach space and henstock-kurzweil integrals
In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.
Differential-algebraic equations in the theory of invariant manifolds for singular equations.
Eine Verallgemeinerung der Riccatischen Differentialgleichung in Körpern der Charakteristik p = 2.
Epidemiological Models With Parametric Heterogeneity : Deterministic Theory for Closed Populations
We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach....
Équations différentielles ordinaires dans les espaces des fonctions bornées
Error estimates and step-size control for the approximate solution of a first order evolution equation
Error estimates of a numerical method for a class of nonlinear evolution equations
Euler polygons and Kneser's theorem for solutions of differential equations in Banach spaces
Evolution differential equations in Fréchet sequence spaces
We consider evolution differential equations in Fréchet spaces with unconditional Schauder basis, and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE are also considered.
Evolution equations governed by families of weighted operators
Evolution equations in discrete and continuous time for nonexpansive operators in Banach spaces
We consider some discrete and continuous dynamics in a Banach space involving a non expansive operator J and a corresponding family of strictly contracting operators Φ (λ, x): = λ J(x) for λ ∈ ] 0,1] . Our motivation comes from the study of two-player zero-sum repeated games, where the value of the n-stage game (resp. the value of the λ-discounted game) satisfies the relation vn = Φ(, ) (resp. = Φ(λ, )) where J is the Shapley operator of the game. We study the evolution equation u'(t) =...
Evolution equations with parameter in the hyperbolic case
The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter in the “hyperbolic” case.