On the Linear Damped Wave Equation

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact Controllability of a Non-linear Generalized Damped Wave Equation: Application to the Sine-gordon Equation

In this paper, we give a sufficient conditions for the exact controllability of the non-linear generalized damped wave equation ẅ + ηẇ + γAw = u(t) + f(t, w, u(t)), on a Hilbert space. The distributed control u ∈ L2 and the operator A is positive definite self-adjoint unbounded with compact resolvent. The nonlinear term f is a continuous function on t and globally Lipschitz in the other variabl...

متن کامل

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 کامل

Eigenvalue Asymptotics, Inverse Problems and a Trace Formula for the Linear Damped Wave Equation

We determine the general form of the asymptotics for Dirichlet eigenvalues of the one–dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion. We also derive a trace formula for this problem.

متن کامل

Finite-dimensional Attractors for the Quasi-linear Strongly-damped Wave Equation

We present a new method of investigating the so-called quasi-linear strongly damped wave equations ∂ t u− γ∂t∆xu−∆xu+ f(u) = ∇x · φ ′(∇xu) + g in bounded 3D domains. This method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity φ is less than 6 and f may have arbitrary polynomial growth rate. Moreover, the existenc...

متن کامل

ذخیره 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 Differential Equations

سال: 1997

ISSN: 0022-0396

DOI: 10.1006/jdeq.1996.3209