Mathematical Models and Methods in Applied Sciences, 1999
ABSTRACT The steady burning stability of solid propellants under thermal radiation with volumetri... more ABSTRACT The steady burning stability of solid propellants under thermal radiation with volumetric absorption is investigated. The combustion model we are dealing with includes the classical assumptions of quasiplanarity of all spatial variations, quasisteadiness of the gas phase and surface reaction. However, the stability analysis requires neither assuming a specific pyrolysis law nor formulating a specific flame submodel as long as the surface mass production and heat feedback satisfy some general properties, which are indeed observed experimentally. The existence of a steady state (traveling wave) solution is proved, and a dispersion relationship for its asymptotic stability is derived by conveniently transforming the problem into an evolution equation in a Banach space. The fully opaque burning surface limit and the case of transparent burning surface with exponential volumetric absorption are examined in details. The resulting stability regions in a proper parameter space are given and, finally, existence and stability of bifurcating time-periodic solutions are discussed.
The authors consider the problem of finding the density of a material body when the strength of t... more The authors consider the problem of finding the density of a material body when the strength of the gravitational field on its surface is known. The continuous dependence of the solution upon datum in L 2 - metrics (i.e., stability) is proved for those densities in a neighborhood of any regular positive solution for which the (harmonic) perturbation term has a bounded gradient.
We give characterizations of the states of thermodynamic equilibrium of infinitely extended and f... more We give characterizations of the states of thermodynamic equilibrium of infinitely extended and finite quantum systems in terms of stability under interactions and of a quantum condition of detailed balance.
A definition of detailed balance for quantum dynamical semigroups is given, and its close connect... more A definition of detailed balance for quantum dynamical semigroups is given, and its close connection with the KMS condition is investigated.
We show, without the use of ad hoc hypotheses and employing only elementary mathematical techniqu... more We show, without the use of ad hoc hypotheses and employing only elementary mathematical techniques, that an equilibrium state of a spatially confined quantum system is described by the Gibbs canonical ensemble, under a stability assumption which amounts essentially to the zeroth law of thermodynamics.
Mathematical Models and Methods in Applied Sciences, 1999
ABSTRACT The steady burning stability of solid propellants under thermal radiation with volumetri... more ABSTRACT The steady burning stability of solid propellants under thermal radiation with volumetric absorption is investigated. The combustion model we are dealing with includes the classical assumptions of quasiplanarity of all spatial variations, quasisteadiness of the gas phase and surface reaction. However, the stability analysis requires neither assuming a specific pyrolysis law nor formulating a specific flame submodel as long as the surface mass production and heat feedback satisfy some general properties, which are indeed observed experimentally. The existence of a steady state (traveling wave) solution is proved, and a dispersion relationship for its asymptotic stability is derived by conveniently transforming the problem into an evolution equation in a Banach space. The fully opaque burning surface limit and the case of transparent burning surface with exponential volumetric absorption are examined in details. The resulting stability regions in a proper parameter space are given and, finally, existence and stability of bifurcating time-periodic solutions are discussed.
The authors consider the problem of finding the density of a material body when the strength of t... more The authors consider the problem of finding the density of a material body when the strength of the gravitational field on its surface is known. The continuous dependence of the solution upon datum in L 2 - metrics (i.e., stability) is proved for those densities in a neighborhood of any regular positive solution for which the (harmonic) perturbation term has a bounded gradient.
We give characterizations of the states of thermodynamic equilibrium of infinitely extended and f... more We give characterizations of the states of thermodynamic equilibrium of infinitely extended and finite quantum systems in terms of stability under interactions and of a quantum condition of detailed balance.
A definition of detailed balance for quantum dynamical semigroups is given, and its close connect... more A definition of detailed balance for quantum dynamical semigroups is given, and its close connection with the KMS condition is investigated.
We show, without the use of ad hoc hypotheses and employing only elementary mathematical techniqu... more We show, without the use of ad hoc hypotheses and employing only elementary mathematical techniques, that an equilibrium state of a spatially confined quantum system is described by the Gibbs canonical ensemble, under a stability assumption which amounts essentially to the zeroth law of thermodynamics.
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