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Group theory --- 517.95 --- Cauchy problem --- Conservation laws (Mathematics) --- Differential equations, Hyperbolic --- Differential equations, Partial --- Partial differential equations --- 517.95 Partial differential equations --- Cauchy problem. --- Cauchy, Problème de --- Lois de conservation (mathématiques) --- Cauchy, Problème de.
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Differential geometry. Global analysis --- Differential equations, Linear --- Cauchy problem --- Équations aux dérivées partielles linéaires --- Cauchy, Problème de --- Cauchy problem. --- Differential equations, Linear. --- Cauchy, Problème de --- Équations aux dérivées partielles linéaires.
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Differential equations --- Differential equations, Hyperbolic --- Differential equations, Nonlinear --- Cauchy problem --- Differential equations, Partial --- Nonlinear differential equations --- Nonlinear theories --- Hyperbolic differential equations --- Differential equations, Hyperbolic. --- Équations différentielles hyperboliques. --- Differential equations, Nonlinear. --- Équations différentielles non linéaires. --- Cauchy problem. --- Cauchy, Problème de.
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Differential equations --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach spaces --- Cauchy [Probleem van ] --- Cauchy [Problème de ] --- Cauchy problem --- Differentiaalvergelijkingen --- Equations différentielles --- Hilbert [Espace d' ] --- Hilbert [Ruimte van ] --- Hilbert space
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Mathematical analysis --- Analyse mathématique --- Cauchy transform. --- Transformation de Cauchy. --- Cauchy-Riemann equations. --- Cauchy-Riemann, Équations de. --- Cauchy problem. --- Cauchy, Problème de. --- Mathematical physics --- Physique mathématique --- Analyse mathématique --- Cauchy-Riemann, Équations de. --- Cauchy, Problème de. --- Physique mathématique
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The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
Banach [Espaces de ] --- Banach [Ruimten van ] --- Banach spaces --- Cauchy [Probleem van ] --- Cauchy [Problème de ] --- Cauchy problem --- Differentiaalvergelijkingen --- Differential equations --- Equations différentielles --- Hilbert [Espace d' ] --- Hilbert [Ruimte van ] --- Hilbert space --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Differential equations. --- Ordinary Differential Equations. --- 517.91 Differential equations
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