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  • 1
    Electronic Resource
    Electronic Resource
    Coagulation-diffusion systems: Derivation and existence of solutions for the diffuse interface structure equations
    Amsterdam : Elsevier
    Physica D: Nonlinear Phenomena 46 (1990), S. 351-366 
    Details
    ISSN: 0167-2789
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0167-2789(90)90098-A
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  • 2
    Electronic Resource
    Electronic Resource
    Scanning control of a vibrating string (1986)
    Springer
    Applied mathematics & optimization 14 (1986), S. 27-47 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct scanning feedback controls {γ i (t)} for the vibrating string equation $$\begin{gathered} y_{tt} (x,t) = y_{xx} (x,t) + Ry(x,t) + \sum\limits_{i = 1}^N {\phi (x - \gamma _i } (t))y(x,t), \hfill \\ 0〈 x〈 1,y = 0 at x = 0,1. \hfill \\ \end{gathered} $$ so that (y, y t ) → (0,0) ast → ∞ in the weak topology ofH 0 1 (0,1) ×L 2 (0,1). In particular we show that ifφ is an even polynomial of degreeN with nonpositive coefficients that forR 〈π 2 we can find such stabilizingγ i (t), i=1,⋯,N.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442226
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  • 3
    Electronic Resource
    Electronic Resource
    Controllability for a class of nondiagonal hyperbolic distributed bilinear systems (1984)
    Springer
    Applied mathematics & optimization 11 (1984), S. 57-76 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper studies controllability of the abstract “hyperbolic” control systemü + Au + p(t)Bu = 0 whereA andB are (possibly) unbounded linear operators on an infinite dimensional Hilbert spaceH andp(t) is a real valued scalar control. The paper gives conditions for elements of the underlying state space to be accessible from prescribed initial data (u(0),57-1 Applications to wave equations are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442170
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  • 4
    Electronic Resource
    Electronic Resource
    Feedback stabilization of distributed semilinear control systems (1979)
    Springer
    Applied mathematics & optimization 5 (1979), S. 169-179 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers feedback stabilization for the semilinear control system $$\dot u(t) = Au(t) + \upsilon (t)B(u(t)).$$ HereA is the infinitesimal generator of a linearC 0 semigroup of contractions on a Hilbert spaceH andB : H → H is a nonlinear operator. A sufficient condition for feedback stabilization is given and applications to hyperbolic boundary value problems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442552
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  • 5
    Electronic Resource
    Electronic Resource
    Book reviews (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 338-340 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00916832
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  • 6
    Electronic Resource
    Electronic Resource
    Renormalization of the Chapman–Enskog Expansion: Isothermal Fluid Flow and Rosenau Saturation (1998)
    Springer
    Journal of statistical physics 91 (1998), S. 285-305 
    Details
    ISSN: 1572-9613
    Keywords: Chapman–Enskog expansion ; Burnett equation ; Boltzmann equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper continues the author's study of procedures for rewriting the well-known Chapman–Enskog expansion used in the kinetic theory of gases. The usual Chapman–Enskog expansion, when used in isothermal fluid motion, will introduce nonlinear instability at super-Burnett order O(ε3) truncation. The procedure given here eliminates the truncation instability and produces the desired dissipation inequality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023048322851
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  • 7
    Electronic Resource
    Electronic Resource
    Metastable fluid flow described via a discrete-velocity coagulation-fragmentation model (1996)
    Springer
    Journal of statistical physics 83 (1996), S. 1067-1108 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; evaporation ; condensation ; cluster ; nucleation ; shock wave ; metastability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A discrete-velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in ℝ3 with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. The model is used to obtain macroscopic fluid equations which are valid into the metastable fluid regime, $$0 \leqslant \rho〈 \rho _s + O(\mu ^\sigma )$$ , where σ is any positive number, μ is the inelastic Knudsen number, andρ s is the saturation density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179553
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamics of measured valued solutions to a backward-forward heat equation (1991)
    Springer
    Journal of dynamics and differential equations 3 (1991), S. 1-28 
    Details
    ISSN: 1572-9222
    Keywords: Measured valued solutions ; backward-forward heat equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper examines the asymptotic behavior of measure valued solutions to the initial value problem for the nonlinear heat conduction equation $$\frac{{\partial u}}{{\partial t}} = \nabla \cdot q(\nabla u), x \in \Omega , t 〉 0$$ ,xεΩ, t〉0 in a bounded domainΩ⊂R N with boundary conditions of the form $$u = 0 on \partial \Omega or q(\nabla u) \cdot n = 0 on \partial \Omega $$ In particular, use of the Young measure representation of composite weak limits allows proof of a general trend to equilibrium. No linearity or monotonicity is assumed forq; the only major restriction onq is that it satisfies the Fourier inequalityq(λ)·λ⩾0 for allλε R N . Applications are given to problems whereq is not monotone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049487
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  • 9
    Electronic Resource
    Electronic Resource
    Instability of steady shearing flows in a non-linear viscoelastic fluid (1978)
    Springer
    Archive for rational mechanics and analysis 68 (1978), S. 211-225 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper proves the non-existence of global smooth solutions to an equation for a viscoelastic fluid shearing flow. The non-existence of smooth solutions is interpreted physically as the formation of a vortex sheet and an instability in the fluid motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00247740
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  • 10
    Electronic Resource
    Electronic Resource
    Positively invariant regions for a problem in phase transitions (1986)
    Springer
    Archive for rational mechanics and analysis 93 (1986), S. 61-79 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Positively invariant regions for the system v t + p(W) x = ɛV xx , W t −V x = ɛW xx are constructed where p′ 〈 0, w 〈 α, w 〉 β, p′(w) = 0, α ≦ w ≦ β, ɛ 〉 0. Such a choice of p is motivated by the Maxwell construction for a van der Waals fluid. The method of an analysis is a modification of earlier ideas of Chueh, Conley, & Smoller [1]. The results given here provide ɛ independent L ∞ bounds on the solution (w, v).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250845
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