𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Approximation of solutions to evolution equations

✍ Scribed by Peter D. Miletta

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
432 KB
Volume
17
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form uβ€²(t)= βˆ’ Au(t) + M(u(t)) is shown. Here A is a closed, positive definite, self‐adjoint linear operator with domain D(A) dense in a Hilbert space H and M is a non‐linear map defined on D(A^Β½^) which satisfies a Lipschitz condition on balls in D(A^Β½^).

πŸ“œ SIMILAR VOLUMES

Generalized Solutions to Fifth-Order Evo
Generalized Solutions to Fifth-Order Evolution Equations
✍ M.M. Melo πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 147 KB

I obtain results of existence and uniqueness of generalized solutions for the Cauchy problem to fifth-order evolution equations such as third member of Korteweg᎐de Vries hierarchy, Olver, Benney, and Fisher equations. I show that my results are associated with the solution obtained by Ponce.

Approximate Solutions of Polynomial Equa
Approximate Solutions of Polynomial Equations
✍ Shih Ping Tung πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 268 KB

In this paper, we introduce "approximate solutions" to solve the following problem: given a polynomial F (x, y) over Q, where x represents an n-tuple of variables, can we find all the polynomials G(x) such that F (x, G(x)) is identically equal to a constant c in Q? We have the following: let F (x, y

Explicit and approximate solutions of se
Explicit and approximate solutions of second-order evolution differential equations in Hilbert space
✍ Ivan P. Gavrilyuk; Vladimir L. Makarov πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 344 KB πŸ‘ 1 views

The explicit closed-form solutions for a second-order differential equation with a constant self-adjoint positive definite operator coefficient A (the hyperbolic case) and for the abstract Euler-Poisson-Darboux equation in a Hilbert space are presented. On the basis of these representations, we prop

Periodic Solutions of Infinite Delay Evo
Periodic Solutions of Infinite Delay Evolution Equations
✍ James H. Liu πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 130 KB

determined by the initial function is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space C , and then derive g periodic solutions from bounded solutions by using Sadovskii's fixed point theorem. This extends the study of deriving periodic solutions from bo