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Mathematische Annalen, ISSN 0025-5831, 8/2016, Volume 365, Issue 3, pp. 969 - 985
... initial data. Mathematics Subject Classification Primary 35L71; Secondary 35B40 1 Introduction Consider the initial value problem for the equation u tt − null u + u e... 
Mathematics, general | Mathematics | Secondary 35B40 | Primary 35L71 | MATHEMATICS
Journal Article
Journal of nonlinear science, ISSN 1432-1467, 2017, Volume 27, Issue 5, pp. 1589 - 1608
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2015, Volume 367, Issue 9, pp. 6557 - 6579
Journal Article
Journal of nonlinear science, ISSN 1432-1467, 2014, Volume 24, Issue 5, pp. 809 - 855
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2017, Volume 68, Issue 2, pp. 1 - 10
...) of Anantharaman and L´ eautaud (Anal PDE 7(1):159–214, 2014, Section 2C). Mathematics Subject Classification. 35B40, 35L05, 47D06. Keywords. Damped wave equation, Piecewise... 
Engineering | 47D06 | Mathematical Methods in Physics | C_0$$ C 0 -semigroups | Energy | Polynomial decay | Piecewise constant damping | 35L05 | Damped wave equation | Resolvent estimates | 35B40 | Theoretical and Applied Mechanics | semigroups | MATHEMATICS, APPLIED | C-0-semigroups | ENERGY DECAY
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 02/2019, Volume 118, Issue 2, pp. 379 - 415
Let Ω be an open bounded domain in Rn with smooth boundary ∂Ω. We consider the equation Δu+un−k+2n−k−2−ε=0inΩ, under zero Dirichlet boundary condition, where ε... 
35J10 | 58C15 (primary) | 35B40 | 35J61 | MATHEMATICS | POSITIVE SOLUTIONS | MINIMAL SUBMANIFOLDS | NEUMANN PROBLEM | BOUNDARY SUBMANIFOLDS | CURVES
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2017, Volume 50, Issue 31, p. 315101
We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators ('nodes') connected by a quantum network... 
quantum synchronization | quantum network | emergence | SchrodingerLohe model | SYSTEM | PHYSICS, MULTIDISCIPLINARY | Schrodinger-Lohe model | PHYSICS, MATHEMATICAL | SCHRODINGER
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 12/2018, Volume 50, Issue 6, pp. 1117 - 1136
We study the long‐time behavior of two vibrating strings which are coupled at a common boundary point by a damper. We show that the classical solutions... 
35B40 (primary) | 47D06 (secondary) | 35L53 | MATHEMATICS | RATES | WAVE-EQUATION | ENERGY DECAY | POINTWISE STABILIZATION | NONUNIFORM
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650038
In this paper, we construct for every α > 0 and λ ∈ ℂ a class of initial values u 0 for which there exists a local solution of the nonlinear Schrödinger... 
Local existence | Global existence | Nonlinear Schrödinger equation | Scattering | MATHEMATICS | MATHEMATICS, APPLIED | global existence | scattering | Nonlinear Schrodinger equation | local existence | CAUCHY-PROBLEM | Analysis of PDEs | Mathematics
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2016, Volume 48, Issue 3, pp. 519 - 532
Abstract We obtain quantified versions of Ingham's classical Tauberian theorem and some of its variants by means of a natural modification of Ingham's own... 
LAPLACE TRANSFORMS | MATHEMATICS | SEMIGROUPS | NONUNIFORM STABILITY | DECAY | Functional Analysis | Mathematics | Classical Analysis and ODEs
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2014, Volume 417, Issue 2, pp. 1018 - 1038
This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space Rn. We first establish the asymptotic... 
Random attractor | Periodic attractor | p-Laplace equation | Pullback attractor | P-Laplace equation | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | Mathematics - Analysis of PDEs
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 6, pp. 2793 - 2824
We consider the wave equation with a boundary condition of memory type. Under natural conditions on the acoustic impedance of the boundary a corresponding... 
Wave equation | Resolvent estimates | [formula omitted]-semigroups | Memory | Decay rates | Viscoelastic damping | semigroups | MATHEMATICS | C-0-semigroups | Mathematics - Analysis of PDEs
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 04/2018, Volume 97, Issue 2, pp. 258 - 281
We consider a convection–diffusion model with linear fractional diffusion in the sub‐critical range. We prove that the large time asymptotic behavior of the... 
35B40 (primary) | 26A33 (secondary) | NONLOCAL REGULARIZATION | MATHEMATICS | DIMENSIONS | CONSERVATION-LAWS | FRACTAL BURGERS-EQUATION | LARGE TIME BEHAVIOR | Mathematics - Analysis of PDEs
Journal Article
Mathematical methods in the applied sciences, ISSN 0170-4214, 2016, Volume 39, Issue 3, pp. 394 - 404
We consider the parabolic chemotaxis model ut=Δu−χ∇·uv∇vvt=Δv−v+u in a smooth, bounded, convex two‐dimensional domain and show global existence and boundedness... 
global existence | singular sensitivity | boundedness | chemotaxis | EXISTENCE | MATHEMATICS, APPLIED | Mathematical models | Energy use | Two dimensional | Mathematical analysis | Proving | Mathematics - Analysis of PDEs
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 9/2016, Volume 16, Issue 3, pp. 649 - 664
We study a simple one-dimensional coupled wave–heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is... 
Wave equation | Rates of decay | Heat equation | Coupled | Energy | Analysis | Resolvent estimates | 47D06 (34K30, 37A25) | Mathematics | 35B40 | C 0 -semigroups | 35M33 | semigroups | MATHEMATICS | RATES | MATHEMATICS, APPLIED | STABILITY | C-0-semigroups
Journal Article
Journal of evolution equations, ISSN 1424-3202, 2018, Volume 18, Issue 4, pp. 1721 - 1744
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 01/2020, Volume 120, Issue 1, pp. 39 - 64
We consider radial solutions of the slightly subcritical problem −Δuε=|uε|4n−2−εuε either on Rn (n⩾3) or in a ball B satisfying Dirichlet or Neumann boundary... 
35J66 (secondary) | 35B40 | 35J25 | 35J15 (primary) | 35B33 | 35B44 | BUBBLE-TOWER SOLUTIONS | MATHEMATICS | SEMILINEAR ELLIPTIC-EQUATIONS | ENERGY NODAL SOLUTIONS | SYMMETRY | BEHAVIOR
Journal Article