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  • 1
    Electronic Resource
    Electronic Resource
    Quantum dynamics study of the Cl+D2 reaction: Time-dependent wave packet calculations (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 7182-7187 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The quantum dynamics of the Cl+D2 reaction has been studied by means of time-dependent quantum wave packet calculations on the G3 and BW2 potential energy surfaces. Initial state-specific total reaction probabilities and integral cross sections are calculated, and the thermal rate constant is obtained. On the G3 surface, the effect of the reagent's rotational excitation on the reactivity is negative, while on the BW2 surface, the rotation of reagent has positive effect on the reactivity. Comparison of the thermal rate constants on the G3 and BW2 surfaces with experimental measurement is shown. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1311799
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On Maxwell's Equations with a Temperature Effect, II (1998)
    Springer
    Communications in mathematical physics 194 (1998), S. 343-358 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: In this paper we study Maxwell's equations with a thermal effect. This system models an induction heating process where the electric conductivity σ strongly depends on the temperature $u$. We focus on a special one–dimensional case where the electromagnetic wave is assumed to be parallel to the y-axis. It is shown that the resulting hyperbolic–parabolic system has a global smooth solution if the electrical conductivity σ(u) grows like u q with 0 ⋚q〈8+4 √ 3. A fundamental element in this paper is the establishment of a maximum principle for wave equations with damping. This maximum principle provides an a priori bound for the first derivative with respect to both $x$ and $t$ of the solution without the imposition of any differentiability assumptions nor bounds on the coefficient of the damping term. The use of a nonlinear multiplier then permits (via a bootstrap procedure) the estimation of successively higher L p -norms of the temperature function u.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050361
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A singular-degenerate free boundary problem arising from the moisture evaporation in a partially saturated porous medium (1992)
    Springer
    Annali di matematica pura ed applicata 161 (1992), S. 379-397 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a moisture evaporation process in a porous medium which is partially saturated by a fluid. The mathematical model is a singular-degenerate nonlinear parabolic free boundary problem. We first transform the problem into a weak form in a fixed domain and then derive some uniform estimates for the proper approximate solution. The existence of a weak solution is established by a compactness argument. Finally, the regularity of the solution and interfaces are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01759646
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Critical Exponents for a System of Heat Equations Coupled in a Non-linear Boundary Condition (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1099-1120 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider a system of heat equations ut = Δu, vt = Δv in an unbounded domain Ω⊂∝N coupled through the Neumann boundary conditions uv = vp, vv = uq, where p〉0, q〉0, pq〉1 and ν is the exterior unit normal on ∂Ω. It is shown that for several types of domain there exists a critical exponent such that all of positive solutions blow up in a finite time in subcritical case (including the critical case) while there exist positive global solutions in the supercritical case if initial data are small.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Determination of an unknown function in a parabolic equation with an overspecified conditionThis work was funded by NSERC Canada. (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 421-430 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the inverse problems of identifying some space-dependent unknown coefficients in parabolic equations subject to initial boundary value conditions along with an overspecified condition at the final time t = T. We use the overspecified information to transform the problems into non-linear parabolic equations involving a functional of the solution with respect to the time variable. This transformation allows us to establish existence theorems for these inverse problems by employing the Schauder fixed-point theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130506
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical solutions of some parabolic inverse problems (1990)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 6 (1990), S. 177-191 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we introduce a variational form by defining a new function. Both continuous and discrete Galerkin procedures are illustrated in this paper. The error estimates are also derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690060207
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    Paper (German National Licenses)
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