zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A one-dimensional wave equation with nonlinear damping. (English) Zbl 1110.35014
The authors consider the following one-dimensional nonlinear wave equation $$u_{tt}- u_{xx}+ \sigma(u) u_t+ g(u)= f,\quad x\in (0,\pi),\quad t> 0,$$ $$u(0,t)= u(\pi, t)= 0,\quad t\in\bbfR^+,$$ $$u(x,0)= u_0(x),\quad u_t(x,0)= u_1(x),\quad x\in (0,\pi),$$ where $f\in L^2(0,\pi)$, $\sigma\in C^1(\bbfR)$ is such that $\sigma(\xi)> 0$, for all $\xi\in\bbfR$. Under the suitable assumptions on the data, the authors prove the existence of a regular connected global attractor. Moreover, they prove the existence of an exponential attractor as well.

35B41Attractors (PDE)
35L70Nonlinear second-order hyperbolic equations
35L20Second order hyperbolic equations, boundary value problems
37L25Inertial manifolds and other invariant attracting sets
37L45Hyperbolicity; Lyapunov functions (infinite-dimensional dissipative systems)
Full Text: DOI