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A Global Existence and Uniqueness Theorem for a Riccati Equation
SIAM Journal on Mathematical Analysis, 1983It is proved that a Riccati differential equation of a particular form has a unique solution satisfying the conditions that it is to exist for large values of the independent variable t and to have its graph stay above a certain line for large t. It is then proved that the solution exists for all t.
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Existence and Uniqueness Theorems for the Boltzmann Equation
1989In general, the situation which arises when mathematically studying the Boltzmann equation may be outlined as follows. There are two well-studied limiting regimes. The first of them is the so-called free-particle flow, where the particles do not interact.
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Existence and Uniqueness Theorems for the Boltzmann Equation
1988The aim of these lecture notes is the presentation of existence theorems for the Boltzmann equation. We do not attempt to give a complete survey of the present state of the theory as two such surveys has been written recently (Fiszdon, Lachowicz, Palczewski [12] and Greenberg, Polewczak, Zweifel [17]). We are rather going to present those results which,
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