Anti-selfdual Lagrangians II: unbounded non self-adjoint operators and evolution equations
نویسندگان
چکیده
منابع مشابه
Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions
We develop the concept and the calculus of anti-selfdual (ASD) Lagrangians and their “potentials” which seem inherent to many partial differential equations and evolutionary systems. They are natural extensions of gradients of convex functions –hence of self-adjoint positive operators– which usually drive dissipative systems, but also provide representations for the superposition of such gradie...
متن کاملNon-self-adjoint Differential Operators
We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...
متن کاملApproximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approxi...
متن کاملIntegrating factors, adjoint equations and Lagrangians
Integrating factors and adjoint equations are determined for linear and nonlinear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by...
متن کاملNon-Self-Adjoint Operators and Pseudospectra
The theory of pseudospectra has grown rapidly since its emergence from within numerical analysis around 1990. We describe some of its applications to the stability theory of differential operators, to WKB analysis and even to orthogonal polynomials. Although currently more a way of looking at non-self-adjoint operators than a list of theorems, its future seems to be assured by the growing numbe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata
سال: 2007
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-007-0046-1