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Entropy in Exact 2D Navier-Stokes and 3D Burgers Gas Flows. [PDF]

Entropy (Basel)
Broadbridge P.
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Controlling linear functional differential equation

Applicable Analysis, 2001
Necessary conditions for the optimal control of a linear system of neutral type functional differential equations are obtained. We show that a success in reducing the initial problem to the problem of solvability of a certain boundary value problem is, in principle, a question of one's ability to construct adjoint operators to the operators appearing ...
Michael Drakhlin, Elena Litsyn
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Large Time Behaviour of Linear Functional Differential Equations

Integral Equations and Operator Theory, 2003
The authors consider linear autonomous functional-differential equations of the type \[ {d\over dt} Dx_t= Lx_t,\quad t\geq 0,\quad x_0= \phi, \] with \(x_t(\theta)= x(t+ \theta)\), \(-r\leq\theta\leq 0\), \[ L\phi= \int^0_{-r} d\eta(\theta\phi(\theta),\quad D\phi= \phi(0)- \int^0_{-r} d\mu(\theta)\phi(\theta). \] Here, \(\theta\), \(\mu\) are \(n\times
Frasson, Miguel V. S., Verduyn Lunel, Sjoerd M.   +1 more
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Linear Functional-Differential Equations with Absolutely Unstable Solutions

Ukrainian Mathematical Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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L p -Perturbation of Linear Functional Differential Equations

Monatshefte f�r Mathematik, 1999
Here, it is shown that a certain class of retarded linear differential equations with solutions of exponential form is stable under \(L^{p}\)-perturbations. An example illustrating this result is given. As a particular case, the asymptotic integration of a class of delay equations of the form \({x'(t)=\sum_{k=0}^{k}}(a_{k}+q_{k}(t))x(t-k\tau)\) is ...
Cassell, J. S., Hou, Zhanyuan
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On Equivalence of Linear Functional-Differential Equations

Results in Mathematics, 1994
The first order ordinary differential equations \(y'(x) = p_0 (x)y(x) + \sum ^k_{i = 1} p_i (x)y (\psi_i (x))\) (with \(k\) deviating arguments, \(k \geq 1\) is fixed) are divided into equivalence classes by means of transformations \(x = h(t)\) and \(z(t) = f(t) y(h(t))\). The author deals with the classes that contains an equation with \(k\) constant
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Non-linear functional differential equations and abstract integral equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1979
SynopsisThe equivalence between solutions of functional differential equations and an abstract integral equation is investigated. Using this result we derive a general approximation result in the state space C and consider as an example approximation by first order spline functions.
Kappel, F., Schappacher, W.
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Linear functional-differential equations on the line

Nonlinear Analysis: Theory, Methods & Applications, 1997
The multidimensional equation \(\sum_{j=1}^{l}(D_jy)(F_jx)=\gamma (x)\) is considered. Here \(x \in {\mathbb{R}^1}\) and \(D_j:C^{\infty }({\mathbb{R}^1}, C^m) \to C^{\infty }({\mathbb{R}^1}, C^m)\) are given linear differential operators. A theory of this equation via ``common dynamics'' of the maps \(F_j\) is built.
Belitskii, G. R., Nicolaevsky, Victor M.
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Slowly varying linear functional differential equations

IEEE Transactions on Automatic Control, 1972
Several authors have studied the stability behavior of slowly varying linear systems of ordinary differential equations. These studies have yielded a sufficient condition for uniform exponential stability. In this work this result is extended to slowly varying linear functional differential equations.
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