Spectral gap global solutions for degenerate Kirchhoff equations
نویسندگان
چکیده
منابع مشابه
Spectral gap global solutions for degenerate Kirchhoff equations
We consider the second order Cauchy problem u +m(|Au|)Au = 0, u(0) = u0, u(0) = u1, where m : [0,+∞) → [0,+∞) is a continuous function, and A is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is well known that this problem admits local-in-time solutions provided that u0 and u1 are regular enough, depending on the continuity modulus of m, and on the strict/weak hyp...
متن کاملDecay of solutions of some degenerate hyperbolic equations of Kirchhoff type
In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction ü = −γu̇+m(‖∇u‖)∆u− δ|u|u+ f, which is known as degenerate if m(·) ≥ 0, and non-degenerate if m(·) ≥ m0 > 0. We would like to point out that, to the author’s knowledge, exponential decay for this type of equations has been studied just for the special cases of α. Our aim ...
متن کاملMildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay
We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dissipative term tends to zero when t → +∞. We prove that the hyperbolic problem has a unique global solution for suitable values of the parameters. We also prove that the solution decays to zero, as t → +∞, with the sam...
متن کاملPeriodic solutions of forced Kirchhoff equations
We consider Kirchhoff equations for vibrating strings and elastic membranes under the action of an external forcing of period 2π/ω and small amplitude ε. We prove existence, regularity and local uniqueness of 2π/ω-periodic solutions of order ε by means of a Nash-Moser iteration scheme; the results hold for parameters (ω, ε) in a Cantor-like set which has asymptotically full measure for ε→ 0.
متن کاملPositive solutions for asymptotically periodic Kirchhoff-type equations with critical growth
In this paper, we consider the following Kirchhoff-type equations: $-left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}, quad mbox{in }mathbb{R}^{3},$ $u(x)>0, quad mbox{in }mathbb{R}^{3},$ $uin H^{1}(mathbb{R}^{3}) ,$ where $a,b>0$ are constants and $lambda$ is a positive parameter. The aim of this paper is to study the existence of positive ...
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: Nonlinear Analysis: Theory, Methods & Applications
سال: 2009
ISSN: 0362-546X
DOI: 10.1016/j.na.2009.02.090