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On Bounding Solutions of Underdetermined Systems
Reliable Computing, 2001For a mapping \(f:D\subseteq R^n\to R^m\), \(m\leq n\), where \(D\) is an open convex set, the author constructs a Krawczyk-Moore-type second-derivative operator (generalizing that one given by \textit{L. Qi} [SIAM J. Numer. Anal. 19, 851-857 (1982; Zbl 0506.65020)] for the case \(m=n\)) which can be used for checking existence and uniqueness of a ...
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Exponential stability and solution bounds for systems with bounded nonlinearities
IEEE Transactions on Automatic Control, 2003Estimation of Lyapunov exponents of systems with bounded nonlinearities plays an essential part in their robust control. Known results in this field are based on the Gronwall inequality yielding relatively conservative bounds for Lyapunov exponents.
Alexandr A. Zevin, Mark A. Pinsky 0002
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ON THE BOUNDNESS OF SOME SOLUTIONS OF THE LÜ SYSTEM
International Journal of Bifurcation and Chaos, 2012By constructing a suitable Lyapunov function, we show that for the Lü chaotic system parameters in some specified regions, the solutions of the system are globally bounded.
Fuchen Zhang, Chunlai Mu, Xiaowu Li
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Principles of Bound Solute Dialysis
Therapeutic Apheresis and Dialysis, 2006Abstract: Toxins that bind to albumin in the bloodstream and are associated with progressing liver failure have proven refractory to removal by conventional hemodialysis. Such toxins can, however, be removed by adding a binder to the dialysate that serves to capture the toxin as it is dialyzed across the membrane.
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Bounded Solutions of Volterra Equations
SIAM Journal on Mathematical Analysis, 1988The author studies the existence of bounded solutions of the equation \[ (1)\quad u'(t)=Au(t)+\int^{\infty}_{0}dB(\tau)u(t-\tau)+f(t),\quad t\in {\mathbb{R}}, \] in a Banach space X. Here A is a closed linear operator with dense domain D(A) and \(B\in BV({\mathbb{R}}_+,B(D(A),X))\).
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Bounds for the solution of hyperbolic problems
Computing, 1987For the equation \(u_{xx}=r(x,y,u,u_ x,u_ y)\), \((x,y)\subseteq {\mathbb{R}}^ 2\), \(u_{| \hat B}=g(x,y)\), \(\hat B\subseteq \partial B\), a method is described for computing guaranteed error bounds for the solution. The basic concepts are: modified fixed point theorems and approximated operators.
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On the upper bound of uniformly bounded solutions
Ukrainian Mathematical Journal, 1994Summary: New conditions of uniform boundedness of solutions are obtained and methods for calculating upper bounds are suggested.
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1998
Abstract The study of the behaviour at infinity of global solutions is one of the most important problems in the study of non-linear evolution equations. The problem can be formulated as follows. If u(t), 0 t < oo is a solution of an equation of the form In the following subsection, we gather some preliminary results that will be ...
Thierry Cazenave +2 more
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Abstract The study of the behaviour at infinity of global solutions is one of the most important problems in the study of non-linear evolution equations. The problem can be formulated as follows. If u(t), 0 t < oo is a solution of an equation of the form In the following subsection, we gather some preliminary results that will be ...
Thierry Cazenave +2 more
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The Bounds of Solutions to Polynomial Complementarity Problems
Journal of Optimization Theory and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xue-liu Li, Guo-ji Tang
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On analyse the behaviour of the solutions on a bounded set
Applied Mathematics and Computation, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Habiba A. Elzohny, Sabah Hafez Abdallah
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