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关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解
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The article was published on 2003-01-01 and is currently open access. It has received 2810 citations till now. The article focuses on the topics: Symbol of a differential operator & Parametrix.read more
Citations
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
TL;DR: In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.
Book
Observation and Control for Operator Semigroups
Marius Tucsnak,George Weiss +1 more
TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
Book
Control and Nonlinearity
TL;DR: In this article, the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions are studied, with a focus on specific phenomena due to nonlinearities.
Book
The Porous Medium Equation: Mathematical Theory
TL;DR: The Porous Medium Equation (PME) as discussed by the authors is one of the classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.
Journal ArticleDOI
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
TL;DR: In this paper, the authors considered the initial value/boundary value problems for fractional diffusion-wave equation and established the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions.
References
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Book
Functional Analysis, Sobolev Spaces and Partial Differential Equations
TL;DR: In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.
Book
Observation and Control for Operator Semigroups
Marius Tucsnak,George Weiss +1 more
TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
Book
Control and Nonlinearity
TL;DR: In this article, the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions are studied, with a focus on specific phenomena due to nonlinearities.
Book
The Porous Medium Equation: Mathematical Theory
TL;DR: The Porous Medium Equation (PME) as discussed by the authors is one of the classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.
Journal ArticleDOI
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
TL;DR: In this paper, the authors considered the initial value/boundary value problems for fractional diffusion-wave equation and established the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions.