Variational methods for nonlinear eigenvalue problems associated with thermal ignition
نویسندگان
چکیده
منابع مشابه
Variational Methods for Nonlinear Elliptic Eigenvalue Problems
In the present note, we give a simple general proof for the existence of solutions of the following two types of variational problems: PROBLEM A. To minimize fa F(x> u, • • • , Du)dx over a subspace VofW>*(tt). PROBLEM B. TO minimize ƒ« F(x, w, • • • , Du)dx for u in V with / a G(x, u, • • • , D^u)dx^c. The solution of the first problem yields a weak solution of a corresponding elliptic boundar...
متن کاملKrylov Methods for Nonlinear Eigenvalue Problems
We present two generalisations of the Krylov subspace method, Arnoldi for the purpose of applying them to nite dimensional eigenvalue problems nonlinear in the eigenvalue parameter. The rst method is called nonlinear rational Krylov subspace and approximates and updates the projection of a linearised problem by nesting a one-sided secant method with Arnoldi. The second method, called nonlinear ...
متن کاملProjection Methods for Nonlinear Sparse Eigenvalue Problems
This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.
متن کاملNonlinear Eigenvalue Problems: A Challenge for Modern Eigenvalue Methods
We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the Jacobi-Davidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to improve structure preservation and wi...
متن کاملAdaptive frame methods for nonlinear variational problems
In this paper we develop adaptive numerical solvers for certain nonlinear variational problems. The discretization of the variational problems is done by a suitable frame decomposition of the solution, i.e., a complete, stable, and redundant expansion. The discretization yields an equivalent nonlinear problem on the space of frame coefficients. The discrete problem is then adaptively solved usi...
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: Journal of Differential Equations
سال: 1973
ISSN: 0022-0396
DOI: 10.1016/0022-0396(73)90017-x