A unitary invariant for pairs of self-adjoint operators.
A universal non-compact operator
A universal property of -semigroups
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .
A useful algebra for functional calculus
We show that some unital complex commutative LF-algebra of -tempered functions on (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.
A Useful Banach Algebra.
A variant of a fixed point theorem of Browder-Fan and Reich.
A variant of Newton's method for generalized equations.
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential...
A variational approach to bifurcation points of a reaction-diffusion system with obstacles and Neumann boundary conditions
Given a reaction-diffusion system which exhibits Turing's diffusion-driven instability, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied. In particular, in some cases it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) bifurcate from a basic spatially homogeneous steady state for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary in the...
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
A version of the Grothendieck theorem for subspaces of analytic functions in lattices.
A viability result for nonconvex semilinear functional differential inclusions
We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
A viability result for second-order differential inclusions.
A Viscoelastic Frictionless Contact Problem with Adhesion
We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution....
A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.
A viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in Hilbert spaces.
A viscosity of Cesàro mean approximation methods for a mixed equilibrium, variational inequalities, and fixed point problems.
A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition on the inertial term. Finally, we provide...
A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.
A weak convergence theorem for total asymptotically pseudocontractive mappings in Hilbert spaces.