Inverse/Observability Estimates for Second-Order Hyperbolic Equations with Variable Coefficients
نویسندگان
چکیده
منابع مشابه
Dispersive and Strichartz estimates for hyperbolic equations with constant coefficients
Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of Lp−Lq norms of propagators are obtained, and it is shown how the time decay rates depend on the geometry of the problem. The frequency space is separated in several zones each giving a certain decay rate. Ge...
متن کاملDiscrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients
This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...
متن کاملStrichartz Estimates for Second Order Hyperbolic Operators with Nonsmooth Coefficients Iii
Denote by x = (x0, x1, ..., xn) = (x0, x′) the coordinates in R × R. Sometimes we refer to the first coordinate x0 as “time” and to x′ as “space” coordinates. The Strichartz estimates for solutions to the homogeneous wave equation in R× R, 2u = 0, u(0) = u0, ut(0) = u1, have the form ‖|D|u‖Lp(Lq) . ‖∇u0‖L2 + ‖u1‖L2. (1.1) Such an estimate holds for all pairs (ρ, p, q) satisfying the relations 2...
متن کاملWeighted L-estimates for Dissipative Wave Equations with Variable Coefficients
We establish weighted L2-estimates for the wave equation with variable damping utt −∆u+ aut = 0 in R, where a(x) ≥ a0(1+ |x|)−α with a0 > 0 and α ∈ [0, 1). In particular, we show that the energy of solutions decays at a polynomial rate t−(n−α)/(2−α)−1 if a(x) ∼ a0|x|−α for large |x|. We derive these results by strengthening significantly the multiplier method. This approach can be adapted to ot...
متن کاملDecay Estimates for Wave Equations with Variable Coefficients
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.
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 Mathematical Analysis and Applications
سال: 1999
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6348