Author | Eidelman, Samuil D. author |
---|---|
Title | Parabolic Boundary Value Problems [electronic resource] / by Samuil D. Eidelman, Nicolae V. Zhitarashu |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8767-0 |
Descript | XI, 300 p. online resource |
I Equations and Problems -- I.1 Equations -- I.2 Initial and boundary value problems -- II Functional Spaces -- II.1 Spaces of test functions and distributions -- II.2 The Hilbert spaces Hs and ?s -- II.3 Banach spaces of Hรถlder functions -- III Linear Operators -- III.1 Operators of potential type -- III.2 Operators of multiplication by a function -- III.3 Commutators. Green formulas -- III.4 On equivalent norms in ?s(?+n+1,?), ?s(E+n+1,?), and Hs(?+n), s ? 0 -- III.5 The spaces $${{\tilde{H}}̂{s}}$$ and $${{\tilde{\mathcal{H}}}̂{s}}$$ -- III.6 Differential operators in the space $${{\tilde{\mathcal{H}}}̂{s}}$$ -- IV Parabolic Boundary Value Problems in Half-Space -- IV.1 Non-homogeneous systems in the space ?++s(?n+1,?) -- IV.2 Initial value and Cauchy problems for parabolic systems in spaces ?s -- IV.3 Model parabolic boundary value problems in $$\bar{\mathbb{R}}_{{ + + }}̂{{n + 1}}$$ -- IV.4 The model boundary value problemin in $$\bar{\mathbb{R}}_{{ + + }}̂{{n + 1}}$$ for general parabolic systems -- IV.5 The model parabolic conjugation problem in classes of smooth functions -- IV.6 Boundary value problem in $$\tilde{\mathcal{H}}_{ + }̂{s}(\bar{\mathbb{R}}_{{ + + }}̂{{n + 1}},\gamma )$$ for operators in which the coefficients of the highest-order derivatives are slowly varying functions -- IV.7 Conjugation problem for operators in which the coefficients of the highest-order derivatives are slowly varying -- V Parabolic Boundary Value Problems in Cylindrical Domains -- V.1 Boundary value problems in a semi-infinite cylinder -- V.2 Nonlocal boundary value problems. Conjugation problems -- V.3 Boundary value problems in cylindrical domains of finite height -- V.4 Solvability of the parabolic boundary value problems for right-hand sides with regular singularities -- V.5 Green formula, boundary and initial values of weak generalized solutions -- VI The Cauchy Problem and Parabolic Boundary Value Problems in Spaces of Smooth Functions -- VI.1 Fundamental solutions of the Cauchy problem -- VI.2 The Cauchy problem -- VI.3 Schauder theory of parabolic boundary value problems -- VI.4 Green functions -- VII Behaviour of Solutions of Parabolic Boundary Value Problems for Large Values of Time -- VII.1 Asymptotic representations and stabilization of solutions of model problems -- VII.2 Tikhonovโs problem -- Comments -- References