Decay estimates for one-dimensional wave equations with inverse power potentials
نویسندگان
چکیده
منابع مشابه
Dispersion Estimates for One-dimensional Schrödinger Equations with Singular Potentials
We derive a dispersion estimate for one-dimensional perturbed radial Schrödinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.
متن کاملDispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schrödinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide new results concerning scattering for one-dimensional discrete perturbed Schrödinger operators which are of independent interest. Most notably we show that the...
متن کاملDecay Estimates for Fourth Order Wave Equations
may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...
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 کاملDecay Estimates for Four Dimensional Schrödinger, Klein-gordon and Wave Equations with Obstructions at Zero Energy
We investigate dispersive estimates for the Schrödinger operator H = −∆+V with V is a real-valued decaying potential when there are zero energy resonances and eigenvalues in four spatial dimensions. If there is a zero energy obstruction, we establish the low-energy expansion eχ(H)Pac(H) = O(1/(log t))A0 +O(1/t)A1 +O((t log t) )A2 +O(t (log t))A3. Here A0, A1 : L (R) → L∞(Rn), while A2, A3 are o...
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: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06345-9