on the new control functions for linear discrete delay systems new control functions are derived for linear difference equations with delay which can be used to construct a nontrivial solution of a boundary value problem with zero boundary conditions later a special case of invariant linear subspace is considered and corresponding control functions are constructed results for weakly nonlinear problems are also discussed

approximate controllability of fractional evolution systems with riemann liouville fractional derivatives in this paper we deal with the control systems governed by fractional evolution differential equations involving riemann liouville fractional derivatives in banach spaces our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions under these conditions the approximate controllability of the associated fractional evolution systems involving riemann liouville fractional derivatives is formulated and proved

relative controllability of fractional delay differential equations via delayed perturbation of mittag leffler functions abstract this paper is concerned with the relative controllability of fractional delay systems in control for finite dimensional spaces a notion of fractional delay grammian matrix involving two parameter mittag leffler type delay matrix function is introduced sufficient and necessary condition is established to examine that linear system is relatively controllable controllability result for semilinear system is obtained by krasnoselskii s fixed point theorem examples are given to illustrate theoretically results

relative and trajectory controllability of linear discrete systems with constant coefficients and a single delay this paper studies the qualitative behavior of solutions of linear discrete systems with constant coefficients and a constant time delay under the influence of a control function in particular it deals with a nontrivial task of transferring an arbitrary solution to several prescribed positions trajectory controllability being more general and different from the problem of relative controllability frequently solved in the literature a kalman type controllability criterion is proved and in addition previous results are discussed and illustrative examples are given

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

a note on relative controllability of higher order linear delayed discrete systems this article is concerned with relative controllability of higher order linear discrete delayed systems with a single delay by a formula that uses special matrix functions discrete delayed matrix sine and cosine to compute the solution of the initial problem a criterion is found for relative controllability in terms of special matrix functions a control function is constructed to solve the problem of relative controllability it is shown that the transformation of a given system into a higher dimensional system without delays leads to a nonequivalent problem of relative controllability the results are illustrated by an example

controllability of linear discrete systems with constant coefficients and pure delay the purpose of this contribution is to develop a controllability method for linear discrete systems with constant coefficients and with pure delay to do this a representation of solutions with the aid of a discrete matrix delayed exponential is used such an approach leads to new conditions of controllability except for a criterion of relative controllability a control function is constructed as well

some qualitative properties of the riemann problem in gas dynamical combustion we study the chapmanjouguet cj model and the selfsimilar zeldovich von neumanndo ring sznd model in chemically reacting gas flows we discover some basic relationships among ignition temperature ti total chemical binding energy q and the adibatic exponent of polytropic gas from these relations we can determine when temperatures along the sznd burning solutions are higher than the ignition temperature ti we also study the all possible selfsimilar solutions for the sznd model from these results we can determine when selfsimilar solutions for the cj model are the limits of selfsimilar solutions of the sznd model when the reaction rate tends to infinity 1997 academic press

moving boundaries in reaction diffusion systems with absorption consider the reaction diffusion system t u d 0 xx u ku 1 v 0 0 t u d 1 xx v ku 1 v with boundary and initial conditions u 0 t c 0 u t 0 t 0 x v 0 t 0 v t 0 u x 0 u 0 x v x 0 v 0 x where 0 u 0 x c 0 and 0 v 0 x 1 for x 0

detonation wave solution to a 1d piston problem for the zeldovich von neumann doring combustion model abstract we consider a one dimensional 1d piston problem for the zeldovich von neumann doring znd combustion model with a one step exothermic chemical reaction this problem can be seen as a riemann initial boundary value problem in order to construct a detonation wave solution to the piston problem we consider a free boundary value problem for the znd model existence of global in time classical solution to this free boundary value problem is obtained by the method of characteristics providing that the binding energy q is sufficiently small

porous medium systems with slow and fast reactions on considere un systeme de trois equations de reaction diffusion faiblement couplees soumises a des conditions aux limites et initiales on donne des theoremes d existence

stability and exponential stability of linear discrete systems with constant coefficients and single delay this paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x k 1 a x k b x k m k 0 1 where a b are square constant matrices and m n sufficient conditions for exponential stability are derived using the method of lyapunov functions and its efficiency is demonstrated by examples

stability and the nonexistence of blowing up solutions of nonlinear delay systems with linear parts defined by permutable matrices abstract sufficient conditions for the exponential stability of the trivial solution of nonlinear differential equations with delay and with linear parts of the form a x t b x t 0 where a b b a are proved a result on the nonexistence of blowing up solutions is also proved

riemann problem for the selfsimilar znd model in gas dynamical combustion abstract all solutions of the riemann problem for the selfsimilar znd combustion model in gas dynamics are constructed that all the cj solutions with entropy conditions in 2 the number of which may be nine for some initial data are the limits of these solutions as the reaction rate goes to infinity is proved

representation of solutions of discrete delayed system x k 1 ax k bx k m f k with commutative matrices abstract in the investigation performed we give on half infinity discrete intervals formulas for solution of initial problem of linear discrete systems x k 1 a x k b x k m f k with constant square matrices a b such that a b b a det a 0 and with a vector function f k corresponding representations are obtained with the aid of so called discrete matrix delayed exponential which permits to represent solutions in a matrix form similarly as for ordinary differential systems with constant matrices or as well as for differential systems with constant matrices and constant delay

uniqueness and ulam stabilities results for partial fractional differential equations with not instantaneous impulses in this paper we investigate some uniqueness and ulam s type stability concepts of fixed point equations for a class of partial functional differential equations with not instantaneous impulses in banach spaces an example is also provided to illustrate our results

exploring delayed mittag leffler type matrix functions to study finite time stability of fractional delay differential equations abstract in this paper we introduce a concept of delayed two parameters mittag leffler type matrix function which is an extension of the classical mittag leffler matrix function with the help of the delayed two parameters mittag leffler type matrix function we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method in addition we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations thereafter we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term finally an example is presented to illustrate the validity of the main theorems

representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via z transform in the present paper a system of nonhomogeneous linear difference equations with any finite number of constant delays and linear parts given by pairwise permutable matrices is considered representation of its solution is derived in a form of a matrix polynomial using the z transform so the recent results for one and two delays and an inductive formula for multiple delays are unified the representation is suitable for theoretical as well as practical computations

a system of singular quasilinear parabolic equations u x 0 u x u k 0 u x o o ifx o if x 0 thus the new feature here is the introduction of nonlinearities to cx and i in fact we only assume that cy and 3 are maximal monotone graphs in r x r these modifications greatly complicate the problem and the techniques of i no longer apply we shall treat the problem from the point of view of the nonlinear semigroup theory the idea is rather simple we regard the vector u ur u2 in the system 1 la as a map from 0 00 into the banach space x l 0 a x l 0 ct define an operator a in x by u v e a if u ur u2 e k c x v u u2 e x and there exist a vector w w w2 in w o a x w2 0 a and a

riemann problem for gasdynamic combustion abstract the riemann problem for gasdynamic combustion is considered existence and uniqueness are obtained constructively for arbitrary riemann data under the following restrictions the solutions are selfsimilar and piecewise smooth the lax entropy condition is satisfied at the discontinuity points except at the front sides of deflagration waves where the temperatures are assumed to be ignition point the number of detonation waves in the solutions is as small as possible the number of times of oscillation of temperature around the ignition point is also as small as possible and last the number of deflagration waves is as large as possible using the riemann problem we analyzed the overtaking of shocks and combustion waves a shock always accelerates detonation whereas it transforms deflagration into detonation when it is strong enough transition from deflagration to detonation in the ignition problem is also investigated

on exponential stability of nonlinear fractional multidelay integro differential equations defined by pairwise permutable matrices in this paper systems of nonlinear differential equations with caputo fractional derivative and multiple delays are considered using representation of a solution of differential equation with multiple delays in the form of matrix polynomial and stability results such as gronwall s and pinto s inequality sufficient conditions for the exponential stability of a trivial solution of nonlinear multidelay fractional differential equations are proved

fredholm s boundary value problems for differential systems with a single delay abstract conditions are derived for the existence of solutions of linear fredholm s boundary value problems for systems of ordinary differential equations with constant coefficients and a single delay utilizing a delayed matrix exponential and a method of pseudo inverse by moore penrose matrices led to an explicit and analytical form of a criterion for the existence of solutions in a relevant space and moreover to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions defined by a linear vector functional not coinciding with the number of unknowns of a differential system with a single delay