Аннотация:
В работе изучаются задача Коши и краевая задача общего вида во внешности компакта для гиперболических операторов L, коэффициенты которых зависят только от x
и постоянны в окрестности бесконечности. В предположении, что волновые фронты матрицы Грина для L уходят при t→∞ на бесконечность, получена асимптотика решений при t→∞. Для соответствующей стационарной задачи получена коротковолновая асимптотика решений для вещественных и комплексных частот.
Эта публикация цитируется в следующих 122 статьяx:
T. J. Christiansen, K. Datchev, M. Yang, “From resolvent expansions at zero to long time wave expansions”, Communications in Partial Differential Equations, 2025, 1
Anjali Jangid, Pooja Devi, Harsh Soni, Aniruddha Chakraborty, “Soliton Solutions for a Quantum Particle in One-dimensional Boxes”, Int J Theor Phys, 63:2 (2024)
Wei Dai, “The global behaviors for defocusing wave equations in two dimensional exterior region”, manuscripta math., 174:1-2 (2024), 59
M. Bernkopf, T. Chaumont-Frelet, J. Melenk, “Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media”, Math. Comp., 2024
А. Ю. Аникин, С. Ю. Доброхотов, В. Е. Назайкинский, М. Руло, “Лагранжевы многообразия и конструкция асимптотик для (псевдо)дифференциальных уравнений с локализованными правыми частями”, ТМФ, 214:1 (2023), 3–29; A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux, “Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides”, Theoret. and Math. Phys., 214:1 (2023), 1–23
А. Ю. Аникин, А. И. Клевин, “Асимптотика решений уравнения Гельмгольца в двухслойной среде с локализованной правой частью”, ТМФ, 216:1 (2023), 148–168; A. Yu. Anikin, A. I. Klevin, “Asymptotics of the Helmholtz equation solutions in a two-layer medium with a localized right-hand side”, Theoret. and Math. Phys., 216:1 (2023), 1036–1054
J. Galkowski, D. Lafontaine, E. A. Spence, J. Wunsch, “Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method”, SIAM J. Math. Anal., 55:4 (2023), 3903
Donald L. Brown, Dietmar Gallistl, “Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wave Number Explicit Bounds”, Computational Methods in Applied Mathematics, 23:1 (2023), 65
Jeffrey Galkowski, David Lafontaine, Euan Spence, “Perfectly-Matched-Layer Truncation is Exponentially Accurate at High Frequency”, SIAM J. Math. Anal., 55:4 (2023), 3344
Théophile Chaumont-Frelet, Andrea Moiola, Euan A. Spence, “Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media”, Journal de Mathématiques Pures et Appliquées, 179 (2023), 183
Ryo Ikehata, “A note on local energy decay results for wave equations with a potential”, ASY, 134:1-2 (2023), 281
Long Yan, Lili Sun, “General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term”, Math Methods in App Sciences, 46:1 (2023), 879
E. A. Spence, J. Wunsch, “Wavenumber-Explicit Parametric Holomorphy of Helmholtz Solutions in the Context of Uncertainty Quantification”, SIAM/ASA J. Uncertainty Quantification, 11:2 (2023), 567
Ryo Ikehata, “L2-blowup estimates of the wave equation and its application to local energy decay”, J. Hyper. Differential Equations, 20:01 (2023), 259
Boussaid N. Comech A., “Limiting Absorption Principle and Virtual Levels of Operators in Banach Spaces”, Ann. Math. Que., 46:1 (2022), 161–180
L. Koralov, S. Molchanov, B. Vainberg, “The radius of a polymer at a near-critical temperature”, Applicable Analysis, 101:8 (2022), 2797
D. Lafontaine, E.A. Spence, J. Wunsch, “Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients”, Computers & Mathematics with Applications, 113 (2022), 59
J. Galkowski, P. Marchand, E. A. Spence, “High-Frequency Estimates on Boundary Integral Operators for the Helmholtz Exterior Neumann Problem”, Integr. Equ. Oper. Theory, 94:4 (2022)
D. Lafontaine, E. A. Spence, J. Wunsch, “A sharp relative-error bound for the Helmholtz h-FEM at high frequency”, Numer. Math., 150:1 (2022), 137
Rajan Puri, Boris Vainberg, “On the critical value of the coupling constant in exterior elliptic problems”, Applicable Analysis, 101:1 (2022), 108