Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation
نویسندگان
چکیده
منابع مشابه
Large Diffusivity Finite-dimensional Asymptotic Behaviour of a Semilinear Wave Equation
We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin-type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second-order ordinary differential equation. In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we pro...
متن کاملAsymptotic behaviour for a semilinear nonlocal equation
We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...
متن کاملFinite Dimensional Null Controllability for the Semilinear Heat Equation
ABSTRACI’. We study a finite dimensional version of the null controllability problem for semilinear heat equations in bounded domains R of R” with Dirichlet boundary conditions. The control acts on any open an non-empty subset of R. The question under consideration is the following: given an initial state, a control time t = 2’ and a finite dimensional subspace E of L”(n), is there a control su...
متن کاملAsymptotic Solutions of Semilinear Stochastic Wave Equations
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponenti...
متن کاملAsymptotic Behavior of Solutions to the Finite-Difference Wave Equation
where up in Eq. (2) corresponds to u(jôx, not) in Eq. (1), and where a = cSt/Sx. Here öt and Sx are the time and space intervals, respectively. We consider the case — co < x < », í > 0. It was shown by Courant, Friedrichs, and Lewy in a wellknown paper [1] that if up and u,x are prescribed for ally, then the computational process represented by Eq. (2) will yield values for w/ which converge to...
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 Applied Mathematics
سال: 2003
ISSN: 1110-757X,1687-0042
DOI: 10.1155/s1110757x03212067