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Journal of Differential Equations, ISSN 0022-0396, 02/2020, Volume 268, Issue 4, pp. 1840 - 1853
We study the long-time behavior of solutions of the -Hessian evolution equation , posed on a bounded domain of the -dimensional space with homogeneous boundary... 
k-Hessian operator | Nonlinear evolution equation | k-admissible solution | Strictly [formula omitted]-convex domain | Self-similar solutions | Asymptotic behavior | MATHEMATICS | ELLIPTIC-EQUATIONS | Strictly (k-1)-convex domain
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 08/2019, Volume 185, pp. 29 - 48
Asymptotic behavior of the higher order spacial derivatives of the strong solution to the incompressible non-stationary magneto-hydrodynamic (MHD) equations is... 
Strong solution | Asymptotic behavior | MHD equation | Half-space | MATHEMATICS, APPLIED | LARGE-TIME BEHAVIOR | L2 DECAY | SPACE | MATHEMATICS | SPATIAL DECAYS | NAVIER-STOKES EQUATIONS | FLOWS | WEAK SOLUTIONS | Economic models | Magnetohydrodynamics | Half spaces | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Hydrodynamic equations
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2017, Volume 450, Issue 1, pp. 152 - 168
This paper concerns the study of the asymptotic behavior of solutions to reaction–diffusion systems modeling multi-components reversible chemistry with spatial... 
Reaction–diffusion equation | Chemical reaction | Entropy method | Asymptotic behavior | Renormalized solution | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | EQUATIONS | MATHEMATICS | ENTROPY METHODS | L-1 | Reaction-diffusion equation | EXPONENTIAL DECAY | EQUILIBRIUM | MASS | Trucks | Four-wheel drive | or physical chemistry | Mathematics | Analysis of PDEs | Chemical Sciences | Theoretical and
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 09/2015, Volume 269, Issue 6, pp. 1714 - 1768
We consider Fisher-KPP equation with advection: for , where and are two free boundaries satisfying Stefan conditions. This equation is used to describe the... 
Fisher-KPP equation | Advection | Free boundary problem | Long time behavior | STEFAN PROBLEM | MATHEMATICS | DIFFUSIVE LOGISTIC MODEL | COMPETITION | GROWTH | FLOW | ASYMPTOTIC-BEHAVIOR | Population biology
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 11, pp. 3671 - 3684
In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed... 
Delay stochastic PDEs | Fractional Brownian motion | Exponential decay in mean square | MATHEMATICS | MATHEMATICS, APPLIED | DRIVEN | Brownian motion | Asymptotic properties | Mathematical analysis | Images | Uniqueness | Evolution | Stochasticity | Delay
Journal Article
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 12/2019, Volume 480, Issue 2, p. 123446
We consider the asymptotic behavior of the global solutions to the initial value problem for the generalized KdV-Burgers equation. It is known that the... 
MATHEMATICS | MATHEMATICS, APPLIED | Second asymptotic profile | Asymptotic behavior | Generalized KdV-Burgers equation | LARGE-TIME BEHAVIOR | Slowly decaying data | DAMPED WAVE-EQUATION
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106099
In this paper, we consider a nonautonomous Choquard equation with singularity where is the Riesz potential of order and , . Under certain assumptions on and ,... 
Singularity | Variational method | Choquard equation | Asymptotic behavior
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 10/2019, Volume 187, pp. 365 - 396
We consider the equation with an additional non-local perturbation term defined through the Hilbert transform, also known as the OST-equation. We prove that... 
Hilbert transform | KdV equation | OST-equation | Decay properties | Persistence problem | STEPANYAMS | MATHEMATICS, APPLIED | OSTROVSKY | TSIMRING EQUATION | CAUCHY-PROBLEM | WELL-POSEDNESS | MATHEMATICS | SOBOLEV SPACES | Decay rate | Perturbation | Asymptotic properties | Hilbert transformation
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2019, Volume 266, Issue 11, pp. 7658 - 7677
This paper studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system with one single diffusion on the whole... 
Fourier splitting technique | Hall-magneto-hydrodynamics | Asymptotic energy oscillation | Long time behavior | MATHEMATICS | GLOBAL EXISTENCE | DECAY | EQUATIONS | CRITERION | WEAK SOLUTIONS | ASYMPTOTIC-BEHAVIOR | Fluid dynamics | Magnetic fields
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 06/2014, Volume 266, Issue 11, pp. 6531 - 6598
In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations... 
Asymptotic behavior of least energy solutions | Fractional Laplacian | Lyapunov–Schmidt reduction | Critical nonlinearity | Lyapunov-Schmidt reduction | BUBBLE | INEQUALITY | EQUATIONS | TOWER | EXTENSION PROBLEM | MATHEMATICS | REGULARITY | HARDY-LITTLEWOOD-SOBOLEV | CRITICAL SOBOLEV EXPONENT | DERIVATIVES | MOVING SPHERES | Energy industry
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2018, Volume 326, pp. 490 - 520
It is known that the Maxwell–Klein–Gordon equations in admit global solutions with finite energy data. In this paper, we present a new approach to study the... 
Maxwell–Klein–Gordon | Large data | Decay | FINITE-ENERGY | DEPENDENT INHOMOGENEOUS-MEDIA | Maxwell-Klein-Gordon | MINKOWSKI SPACE | ASYMPTOTIC PROPERTIES | WELL-POSEDNESS | YANG-MILLS EQUATIONS | MATHEMATICS | DIMENSIONS | FIELD-EQUATIONS | WAVE-EQUATIONS
Journal Article
Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 12/2018, Volume 49, Issue 4, pp. 601 - 620
We study asymptotic behavior of solutions to an initial value problem posed for heat equation. For which, we construct an approximate solution to the initial... 
heat equation | Numerical Analysis | Asymptotic behavior | Mathematics, general | Mathematics | Cole-Hopf transformation | Applications of Mathematics | MATHEMATICS | CONVERGENCE | Asymptotic expansions | Boundary value problems | Research | Heat equation | Mathematical research
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 02/2016, Volume 41, Issue 2, pp. 282 - 317
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 07/2017, Volume 353, Issue 1, pp. 135 - 184
We give asymptotics for the Einstein vacuum equations in wave coordinates with small asymptotically flat data. We show that the behavior is wave like at null... 
EXISTENCE | LIFE-SPAN | BLOW-UP | NULL CONDITION | PHYSICS, MATHEMATICAL | GLOBAL-SOLUTIONS
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 08/2019, Volume 48, pp. 54 - 70
In this paper, we consider a class of fourth-order parabolic equation modeling epitaxial growth. For the evolution problem, we study the exponential decay of... 
Fourth order parabolic equation | Epitaxial growth | Ground-state solution | Exponential decay | MATHEMATICS, APPLIED | Epitaxy | Models | Lagrange multiplier | Modelling | Lagrange multipliers | Asymptotic properties
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2019, Volume 98, pp. 95 - 100
In this paper, we study the Cauchy problem of the Cahn–Hilliard equation, and first reveal that the complicated asymptotic behavior of solutions can happen in... 
Majorizing kernel | Commutation relation | Cahn–Hilliard equation | Asymptotic behavior | Cahn-Hilliard equation | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 12/2019, Volume 189, p. 111573
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 10, pp. 4907 - 4930
In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion... 
Asymptotic stability | Free boundary problem | Tumor spheroid | Gibbs–Thomson relation | Well-posedness | MATHEMATICS | INSTABILITY | SYMMETRY-BREAKING BIFURCATIONS | STABILITY | STATIONARY SOLUTIONS | GROWTH | Gibbs Thomson relation | INHIBITORS | Models | Tumors
Journal Article
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