Some Aspects of Cauchy's Problem PDF Download

Author: Elinar Hille
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 20

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Author: Elinar Hille
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 9

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Author: Irina V. Melnikova
Publisher: CRC Press
ISBN: 1420035495
Category : Mathematics
Languages : en
Pages : 259

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Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat

Author: Sigeru Mizohata
Publisher: Academic Press
ISBN: 148326906X
Category : Mathematics
Languages : en
Pages : 186

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Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.

Author: Lars Gårding
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 322

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Author: Anneli Lax
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :

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Author: Ti-Jun Xiao
Publisher:
ISBN: 9783662178607
Category :
Languages : en
Pages : 324

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Author: Jacques Hadamard
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 336

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Author: Ti-Jun Xiao
Publisher: Springer
ISBN: 3540494790
Category : Mathematics
Languages : en
Pages : 314

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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.

Author: Jacques Hadamard
Publisher:
ISBN:
Category : Cauchy problem
Languages : en
Pages : 336

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