We introduce a sort of semilinear structure on subsets of the family of semigroups defined on a m... more We introduce a sort of semilinear structure on subsets of the family of semigroups defined on a metric space. The key step is the definition of the sum of two semigroups, which is here achieved by means of the classical operator splitting technique. No linearity assumption is required, since the whole construction is in a metric space.
Here t > 0 and x ∈ R; moreover v > 0 is the specific volume, u the velocity, λ the mass density f... more Here t > 0 and x ∈ R; moreover v > 0 is the specific volume, u the velocity, λ the mass density fraction of vapor in the fluid. Then λ ∈ [0, 1], with λ = 0 characterizes the liquid and λ = 1 the vapor phase; intermediate values of λ model mixtures of the two pure phases. The pressure is p = p(v, λ); under natural assumptions the system is strictly hyperbolic. We refer to [4, 3] for more information on the model. System (1) has close connections to a system considered by Peng [6]. A comparison of the two models is done in [1].
We introduce a sort of semilinear structure on subsets of the family of semigroups defined on a m... more We introduce a sort of semilinear structure on subsets of the family of semigroups defined on a metric space. The key step is the definition of the sum of two semigroups, which is here achieved by means of the classical operator splitting technique. No linearity assumption is required, since the whole construction is in a metric space.
Here t > 0 and x ∈ R; moreover v > 0 is the specific volume, u the velocity, λ the mass density f... more Here t > 0 and x ∈ R; moreover v > 0 is the specific volume, u the velocity, λ the mass density fraction of vapor in the fluid. Then λ ∈ [0, 1], with λ = 0 characterizes the liquid and λ = 1 the vapor phase; intermediate values of λ model mixtures of the two pure phases. The pressure is p = p(v, λ); under natural assumptions the system is strictly hyperbolic. We refer to [4, 3] for more information on the model. System (1) has close connections to a system considered by Peng [6]. A comparison of the two models is done in [1].
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Papers by Andrea Corli