Damped wave equation with a critical nonlinearity
نویسندگان
چکیده
منابع مشابه
Damped Wave Equation with a Critical Nonlinearity
We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity { ∂2 t u+ ∂tu−∆u+ λu 2 n = 0, x ∈ Rn, t > 0, u(0, x) = εu0 (x) , ∂tu(0, x) = εu1 (x) , x ∈ Rn, where ε > 0, and space dimensions n = 1, 2, 3. Assume that the initial data u0 ∈ H ∩H, u1 ∈ Hδ−1,0 ∩H−1,δ, where δ > n 2 , weighted Sobolev spaces are H = { φ ∈ L; ...
متن کاملGlobal stability of travelling fronts for a damped wave equation with bistable nonlinearity
We consider the damped wave equation αutt +ut = uxx−V ′(u) on the whole real line, where V is a bistable potential. This equation has travelling front solutions of the form u(x, t) = h(x − st) which describe a moving interface between two different steady states of the system, one of which being the global minimum of V . We show that, if the initial data are sufficiently close to the profile of...
متن کاملAttractor and Dimension for Discretization of a Damped Wave Equation with Periodic Nonlinearity
The existence and Hausdorff dimension of the global attractor for discretization of a damped wave equation with the periodic nonlinearity under the periodic boundary conditions are studied for any space dimension. The obtained Hausdorff dimension is independent of the mesh sizes and the space dimension and remains small for large damping, which conforms to the physics.
متن کاملA Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کاملOn a geometric equation with critical nonlinearity on the boundary
A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a C2 function H to be the mean curvature of some conformal scalar flat metric is that H is positive somewhere. We show that, when the boundary is umbilic and the fu...
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: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-05-03818-3