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Well-Posedness of Parabolic Difference Equations

Well-Posedness of Parabolic Difference Equations

A. Ashyralyev / P.E. Sobolevskii / A. Iacob

120,05 €
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Editorial:
Springer Nature B.V.
Año de edición:
2012
Materia
Cálculo y análisis matemático
ISBN:
9783034896610
120,05 €
IVA incluido
Disponible

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Sobre IBD

A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.

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Otros libros del autor

  • Well-Posedness of Parabolic Difference Equations
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    1 The Abstract Cauchy Problem.- 1. Well-Posedness of the Differential Cauchy Problem in C(E).- 1. The Cauchy problem in a Banach space E. Definition of well-posedness in C(E).- 2. Examples of well-posed and ill-posed problems in C(E).- 3. The homogeneous equation. Strongly continuous semigroups.- 4. The nonhomogeneous equation. Analytic semigroups.- 5. Well-posedness in C(E) of...
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