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Journal of Fourier Analysis and Applications, ISSN 1069-5869, 10/2019, Volume 25, Issue 5, pp. 2447 - 2462
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 10/2018, Volume 136, Issue 1, pp. 209 - 251
We study the spectral asymptotics of wave equations on certain compact spacetimes, where some variant of the Weyl asymptotic law is valid. The simplest example... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | PRODUCTS | OPERATORS | WEYL ASYMPTOTICS | Operators (mathematics) | Wave propagation | Asymptotic properties | Mathematical analysis | Spacetime | Wave equations | Eigenvalues | Eigen values
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 15
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 3/2013, Volume 16, Issue 1, pp. 262 - 272
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 10/2014, Volume 124, Issue 1, pp. 1 - 38
We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | EXISTENCE | SPACE | MATHEMATICS | DECAY | CAUCHY-PROBLEM | ANGULAR REGULARITY | SCATTERING | POSEDNESS | Nonlinearity | Schroedinger equation | Mathematical analysis | Estimates | Scattering | Wave equations
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2017, Volume 40, Issue 14, pp. 5131 - 5140
In this paper, we consider an wave equation in the presence of memory. The viscoelastic kernel g(t) is subject to a general assumption g′(t)⩽−H(g(t)), where... 
intrinsic decay rate | abstract wave equation | memory term | MATHEMATICS, APPLIED | ENERGY | STABILITY | VISCOELASTIC EQUATION | DISSIPATIVE SYSTEMS | GENERAL DECAY | Viscoelasticity | Decay rate | Dissipation
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 6/2019, Volume 70, Issue 3, pp. 1 - 25
We consider the stability of a system of two strongly coupled wave equations by means of only one boundary feedback. We show that the stability of the system... 
Wave equation | Theoretical and Applied Mechanics | Exponential stability | 35L53 | Engineering | Mathematical Methods in Physics | Transmission of boundary dissipation | 93D20 | 93D15 | Polynomial energy decay rate | 35B40 | 93C20 | Indirect damping | POLYNOMIAL DECAY | RATES | MATHEMATICS, APPLIED | ENERGY DECAY-RATE | STABILITY | ABSTRACT SYSTEM
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 10/2017, Volume 133, Issue 1, pp. 91 - 131
For the radial energy-supercritical nonlinear wave equation □u = −u tt + Δu = ±u 7 on R3+1, we prove the existence of a class of global in forward time C... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | Nonlinear equations | Regularization | Wave equations | Self-similarity
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 9/2015, Volume 127, Issue 1, pp. 219 - 246
We study one-dimensional wave equations defined by a class of fractal Laplacians. These Laplacians are defined by fractal measures generated by iterated... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | SELF-SIMILAR MEASURES | HEAT KERNELS | EIGENVALUE BEHAVIOR | EIGENFUNCTIONS | GAPS | OPERATORS | Computer science
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 14
We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude... 
abstract wave equation | nonexistence | 35L70 | global solutions | 35B35 | Analysis | high energies | Mathematics, general | blow up | Mathematics | Applications of Mathematics | 35B40 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | INSTABILITY | GENERALIZED BOUSSINESQ EQUATION | POSITIVE-ENERGY | TIME BLOW-UP | Wave equations | Research
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 6/2013, Volume 19, Issue 3, pp. 514 - 544
Journal Article
Electronic Journal of Differential Equations, ISSN 1072-6691, 12/2016, Volume 2016, Issue 334, pp. 1 - 17
In this article we prove convergence to equilibrium and decay estimates for a class of damped abstract wave equations. We focus on the damping term to be as... 
Decay estimates | Convergence to equilibrium | Abstract wave equation | Łojasiewicz inequality | DISSIPATION | MATHEMATICS, APPLIED | decay estimates | Lojasiewicz inequality | EVOLUTION-EQUATIONS | MATHEMATICS | ANALYTIC NONLINEARITY | EQUILIBRIUM | convergence to equilibrium | CONVERGENCE | SYSTEMS | BOUNDED SOLUTIONS
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 8/2018, Volume 24, Issue 4, pp. 1000 - 1036
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 3, pp. 2259 - 2274
We prove convergence to a stationary solution as time goes to infinity of solutions to abstract nonlinear wave equation with general damping term and gradient... 
Abstract wave equation with damping | Convergence to equilibrium | Łojasiewicz inequality | SYSTEM | MATHEMATICS | NONLINEAR DISSIPATION | ANALYTIC NONLINEARITY | Lojasiewicz inequality | BOUNDED SOLUTIONS | Numerical analysis
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 9/2014, Volume 17, Issue 3, pp. 881 - 896
Journal Article