Calculus of variations and partial differential equations, ISSN 1432-0835, 2014, Volume 52, Issue 1-2, pp. 199 - 235

We study the nonlocal equation $$\begin{aligned} -\varepsilon ^2 \Delta u_\varepsilon +V u_\varepsilon = \varepsilon ^{-\alpha }\bigl (I_\alpha *|u_\varepsilon...

35B25 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35Q55 | Secondary 35B09 | Mathematics | 45K05 | 35B40 | Primary 35J61 | Mathematics Subject Classification : Primary 35J61, Secondary 35B09, 35B25, 35B33, 35B40, 35Q55, 45K05 | EXISTENCE | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | BOUND-STATES | DECAY | STANDING WAVES | CRITICAL FREQUENCY | NEWTON EQUATIONS | POTENTIALS | GRAVITY | Variational methods | Partial differential equations | Mathematical analysis | Proving | Decay | Texts | Calculus of variations | Optimization | Mathematics - Analysis of PDEs

35B25 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35Q55 | Secondary 35B09 | Mathematics | 45K05 | 35B40 | Primary 35J61 | Mathematics Subject Classification : Primary 35J61, Secondary 35B09, 35B25, 35B33, 35B40, 35Q55, 45K05 | EXISTENCE | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | BOUND-STATES | DECAY | STANDING WAVES | CRITICAL FREQUENCY | NEWTON EQUATIONS | POTENTIALS | GRAVITY | Variational methods | Partial differential equations | Mathematical analysis | Proving | Decay | Texts | Calculus of variations | Optimization | Mathematics - Analysis of PDEs

Journal Article

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

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

... behavior Mathematics Subject Classiﬁcation Primary 76D05; Secondary 35B40 Communicated by Paul Newton. This work was performed within the framework of the LABEX MILYON...

The Boussinesq equation and asymptotic behavior | Secondary 35B40 | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Mathematical and Computational Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | Kato spaces | Mathematics | Primary 76D05 | SPACE | MATHEMATICS, APPLIED | MECHANICS | DECAY | EQUATIONS | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Force and energy | Mathematics - Analysis of PDEs

The Boussinesq equation and asymptotic behavior | Secondary 35B40 | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Mathematical and Computational Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | Kato spaces | Mathematics | Primary 76D05 | SPACE | MATHEMATICS, APPLIED | MECHANICS | DECAY | EQUATIONS | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Force and energy | Mathematics - Analysis of PDEs

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2013, Volume 265, Issue 2, pp. 153 - 184

We consider a semilinear elliptic problem−Δu+u=(Iα⁎|u|p)|u|p−2uinRN, where Iα is a Riesz potential and p>1. This family of equations includes the Choquard or...

Pohožaev identity | Stationary nonlinear Schrödinger–Newton equation | Stationary Hartree equation | Decay asymptotics | Nonlocal semilinear elliptic problem | Stationary Choquard equation | Riesz potential | Existence | Symmetry | Stationary nonlinear Schrödinger-Newton equation | Stationary nonlinear Schrodinger-Newton equation | SYMMETRIZATION | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | Pohozaev identity | MATHEMATICS | SCHRODINGER-NEWTON EQUATIONS | Mathematics - Analysis of PDEs

Pohožaev identity | Stationary nonlinear Schrödinger–Newton equation | Stationary Hartree equation | Decay asymptotics | Nonlocal semilinear elliptic problem | Stationary Choquard equation | Riesz potential | Existence | Symmetry | Stationary nonlinear Schrödinger-Newton equation | Stationary nonlinear Schrodinger-Newton equation | SYMMETRIZATION | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | Pohozaev identity | MATHEMATICS | SCHRODINGER-NEWTON EQUATIONS | Mathematics - Analysis of PDEs

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2015, Volume 367, Issue 9, pp. 6557 - 6579

where I_\alpha in the spirit of Berestycki and Lions. This solution is a groundstate and has additional local regularity properties; if moreover F (0,\infty )...

Polarization | Pohožaev identity | Mountain pass | Stationary Hartree equation | Stationary nonlinear Schrödinger–Newton equation | Variational method | Nonlocal semilinear elliptic problem | Existence | Groundstate | Riesz potential | Stationary Choquard equation | Symmetry | MATHEMATICS | R-N | SCALAR FIELD-EQUATIONS | SYMMETRY | SYMMETRIZATION | SCHRODINGER-NEWTON EQUATIONS | COMPACTNESS | POLARIZATION | CRITICAL-POINTS | Mathematics - Analysis of PDEs

Polarization | Pohožaev identity | Mountain pass | Stationary Hartree equation | Stationary nonlinear Schrödinger–Newton equation | Variational method | Nonlocal semilinear elliptic problem | Existence | Groundstate | Riesz potential | Stationary Choquard equation | Symmetry | MATHEMATICS | R-N | SCALAR FIELD-EQUATIONS | SYMMETRY | SYMMETRIZATION | SCHRODINGER-NEWTON EQUATIONS | COMPACTNESS | POLARIZATION | CRITICAL-POINTS | Mathematics - Analysis of PDEs

Journal Article

Journal of nonlinear science, ISSN 1432-1467, 2014, Volume 24, Issue 5, pp. 809 - 855

We consider nonnegative solutions of the Neumann initial-boundary value problem for the chemotaxis-growth system $$\begin{aligned} \left\{ \begin{array}{l}...

35A07 | Secondary: 35F30 | Theoretical, Mathematical and Computational Physics | Hyperbolic-elliptic system | Mathematics | 92C17 | Chemotaxis | 35K55 | Blow-up | Analysis | Appl.Mathematics/Computational Methods of Engineering | Mechanics | Logistic source | Primary: 35B40 | Economic Theory | MATHEMATICS, APPLIED | KELLER-SEGEL SYSTEM | INVASION | MECHANICS | TISSUE | ATTRACTOR | PHYSICS, MATHEMATICAL | TIME BLOW-UP

35A07 | Secondary: 35F30 | Theoretical, Mathematical and Computational Physics | Hyperbolic-elliptic system | Mathematics | 92C17 | Chemotaxis | 35K55 | Blow-up | Analysis | Appl.Mathematics/Computational Methods of Engineering | Mechanics | Logistic source | Primary: 35B40 | Economic Theory | MATHEMATICS, APPLIED | KELLER-SEGEL SYSTEM | INVASION | MECHANICS | TISSUE | ATTRACTOR | PHYSICS, MATHEMATICAL | TIME BLOW-UP

Journal Article

Potential Analysis, ISSN 0926-2601, 8/2019, Volume 51, Issue 2, pp. 255 - 289

We study large time behavior of renormalized solutions of the Cauchy problem for equations of the form ∂ t u − L u + λ u = f(x, u) + g(x, u) ⋅ μ, where L is...

Dirichlet operator | Mesure data | Backward stochastic differential equation | Probability Theory and Stochastic Processes | Mathematics | 35K58 | Semilinear equation | Geometry | Potential Theory | Functional Analysis | Large time behavior of solutions | Primary: 35B40 | Secondary: 60H30 | Rate of convergence | EXISTENCE | FORMS | MATHEMATICS | SYSTEMS | NATURAL GROWTH TERMS | ELLIPTIC-EQUATIONS | Computer science | Differential equations | Mathematics - Analysis of PDEs

Dirichlet operator | Mesure data | Backward stochastic differential equation | Probability Theory and Stochastic Processes | Mathematics | 35K58 | Semilinear equation | Geometry | Potential Theory | Functional Analysis | Large time behavior of solutions | Primary: 35B40 | Secondary: 60H30 | Rate of convergence | EXISTENCE | FORMS | MATHEMATICS | SYSTEMS | NATURAL GROWTH TERMS | ELLIPTIC-EQUATIONS | Computer science | Differential equations | Mathematics - Analysis of PDEs

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

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

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

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

35B40 (primary) | 47D06 (secondary) | 35L53 | MATHEMATICS | RATES | WAVE-EQUATION | ENERGY DECAY | POINTWISE STABILIZATION | NONUNIFORM

Journal Article

12.
Full Text
Local existence, global existence, and scattering for the nonlinear Schrödinger equation

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

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

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

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

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

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

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

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

We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate...

Perturbed wave equation | C 0-semigroup | Fourier multiplier | Polynomial growth | Kreiss condition | Positive semigroup | Primary 47D06 | Analysis | Mathematics | 35B40 | 42B15 | Secondary 34D05 | C_{0}$$ C 0 -semigroup | semigroup | MATHEMATICS, APPLIED | C-0-SEMIGROUPS | SPACES | STABILITY | BOUNDEDNESS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | C-0-semigroup | POSITIVE SEMIGROUPS | FOURIER MULTIPLIER THEOREMS | DISCRETE | Research institutes

Perturbed wave equation | C 0-semigroup | Fourier multiplier | Polynomial growth | Kreiss condition | Positive semigroup | Primary 47D06 | Analysis | Mathematics | 35B40 | 42B15 | Secondary 34D05 | C_{0}$$ C 0 -semigroup | semigroup | MATHEMATICS, APPLIED | C-0-SEMIGROUPS | SPACES | STABILITY | BOUNDEDNESS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | C-0-semigroup | POSITIVE SEMIGROUPS | FOURIER MULTIPLIER THEOREMS | DISCRETE | Research institutes

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

35J66 (secondary) | 35B40 | 35J25 | 35J15 (primary) | 35B33 | 35B44 | BUBBLE-TOWER SOLUTIONS | MATHEMATICS | SEMILINEAR ELLIPTIC-EQUATIONS | ENERGY NODAL SOLUTIONS | SYMMETRY | BEHAVIOR

Journal Article