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An existence and uniqueness theorem in linear elastodynamics
Meccanica, 1975Laplace transform with respect to time is applied to the boundary-initial-value problem of linear elastodynamics in order to produce a simpler elliptic boundary-value problem. Existence and uniqueness of the weak solution of the latter problem are proved.
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An existence and uniqueness theorem for the Vlasov‐Maxwell system
Communications on Pure and Applied Mathematics, 1984The purpose of the present paper is to give a local existence and uniqueness theorem for the Vlasov-Maxwell system of equations, which is one of the fundamental sets of equations underlying the kinetic theory of plasma. It is a nonlinear integro-differential system which describes the collective motion of charged particles in the presence of their own ...
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A theorem of existence and uniqueness in nonlinear optics
1979We consider quasilinear hyperbolic systems of canonical form with boundary conditions for which L. Cesari [Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (1974), 311-358 (1975)] proved an existence and uniqueness theorem requiring among other assumptions that the two k×k matrices involved have "dominant main diagonal'' in a suitable sense and a parameter a is ...
P. BASSANINI, SALVATORI, Maria Cesarina
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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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