Decay Estimates for Wave Equations with Variable Coefficients

نویسندگان

  • PETRONELA RADU
  • BORISLAV YORDANOV
چکیده

We establish weighted L2−estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the L2−norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Generalized Diffusion Phenomenon and Applications

We study the asymptotic behavior of solutions to dissipative wave equations involving two non-commuting self-adjoint operators in a Hilbert space. The main result is that the abstract diffusion phenomenon takes place, as solutions of such equations approach solutions of diffusion equations at large times. When the diffusion semigroup has the Markov property and satisfies a Nash-type inequality,...

متن کامل

Higher Order Energy Decay Rates for Damped Wave Equations with Variable Coefficients Petronela Radu, Grozdena Todorova and Borislav Yordanov

Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x) has been shown to decay. Determining the rate of decay for the higher order energies involving the kth order spatial and time derivatives has been an open problem with the exception of some sparse results obtained for k = 1, 2, 3. We establish estimat...

متن کامل

Higher Order Energy Decay Rates for Damped Wave Equations with Variable Coefficients

Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x, t) has been shown to decay. Determining the decay rate for the higher order energies of the kth order spatial and time derivatives has been an open problem with the exception of some sparse results obtained for k = 1, 2. We establish the sharp gain in...

متن کامل

Decay Estimates for Variable Coefficient Wave Equations in Exterior Domains

In this article we consider variable coefficient, time dependent wave equations in exterior domains R × (R \ Ω), n ≥ 3. We prove localized energy estimates if Ω is star-shaped, and global in time Strichartz estimates if Ω is strictly convex.

متن کامل

Improved Estimates of Kinematic Wave Parameters for Circular Channels

The momentum equation in the kinematic wave model is a power-law equation with two parameters. These parameters, which relate the discharge to the flow area, are commonly derived using Manning’s equation. In general, the values of these parameters depend on the flow depth except for some special cross sections. In this paper, improved estimates of the kinematic wave parameters for circular chan...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008