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Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2018, Volume 462, Issue 2, pp. 1679 - 1694
This paper is concerned with a stability problem for compressible Navier–Stokes–Poisson systems. It arises in the modeling of semiconductors with a viscosity... 
Steady-state | Energy estimate | Global smooth solution | Navier–Stokes–Poisson system | MATHEMATICS | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | NONCONSTANT EQUILIBRIUM SOLUTIONS | SEMICONDUCTORS | EQUATIONS | MODEL | Navier-Stokes-Poisson system
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 04/2012, Volume 65, Issue 4, pp. 549 - 585
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier‐Stokes equations in three... 
SPACE | MATHEMATICS | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | BEHAVIOR | VISCOUS FLUIDS | BLOW-UP | WEAK SOLUTIONS | FLOW | DISCONTINUOUS INITIAL DATA | UNIQUENESS
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2017, Volume 68, Issue 5, pp. 1 - 17
This paper is concerned with a stability problem in a periodic domain for a non-isentropic Euler–Maxwell system without temperature diffusion term. This system... 
Engineering | Mathematical Methods in Physics | Stability | Steady-state solution | Energy estimate | Global smooth solution | 35Q35 | Euler–Maxwell system | 35B40 | Theoretical and Applied Mechanics | 35Q60 | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | GLOBAL EXISTENCE | NONCONSTANT EQUILIBRIUM SOLUTIONS | EQUATIONS | MODEL | Euler-Maxwell system
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2016, Volume 135, pp. 57 - 72
We study a Keller–Segel type of system, which includes growth and death of the chemotactic species and an elliptic equation for the chemo-attractant. The... 
Chemotaxis–growth system | Global solutions | Hyperbolic–elliptic system | Blowup | Parabolic–elliptic system | Parabolic-elliptic system | Chemotaxis-growth system | Hyperbolic-elliptic system | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BOUNDEDNESS | DIFFUSION | Chemotherapy | Cancer | Death | Nonlinearity | Convexity | Mathematical analysis | Smooth boundaries | Constraining
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2016, Volume 55, Issue 4, pp. 1 - 39
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2019, Volume 361, pp. 689 - 702
This paper has attended to obtain the approximate analytical expressions of periodic solutions in the delayed non-smooth Internet TCP-RED congestion control... 
Chaos | HB-AFT | TCP-RED congestion control system | Delayed non-smooth | Periodic solutions | MATHEMATICS, APPLIED | HARMONIC-BALANCE ANALYSIS | CONTROL MODEL | STABILITY | BIFURCATION | Transmission Control Protocol/Internet Protocol (Computer network protocol) | Control systems | Numerical analysis
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 05/2016, Volume 26, Issue 5, pp. 987 - 1024
We consider the chemotaxis system {u(t) = Delta u - del . (u/v del u), v(t) = Delta v - uv, as originally introduced in 1971 by Keller and Segel in the second... 
generalized solutions | global existence | stabilization | Chemotaxis | EXISTENCE | MATHEMATICS, APPLIED | CHEMOTAXIS SYSTEM | EQUATIONS | MODEL | TRAVELING-WAVES | NONLINEAR STABILITY | BLOW-UP | HYPERBOLIC-PARABOLIC SYSTEM | REINFORCED RANDOM-WALKS
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 9/2019, Volume 370, Issue 2, pp. 475 - 505
Using recent developments in the theory of globally defined expanding compressible gases, we construct a class of global-in-time solutions to the compressible... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | EXISTENCE | SMOOTH SOLUTIONS | PHYSICAL VACUUM | MOTION | STABILITY | NONLINEAR INSTABILITY | EQUATIONS | GAS | WELL-POSEDNESS | PHYSICS, MATHEMATICAL
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 3/2018, Volume 227, Issue 3, pp. 995 - 1059
For the three-dimensional full compressible Navier–Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic... 
Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | MECHANICS | VISCOUS-GAS | EQUATIONS | FLOWS | HEAT-CONDUCTING FLUIDS
Journal Article
NONLINEARITY, ISSN 0951-7715, 06/2019, Volume 32, Issue 6, pp. 2201 - 2225
We investigate the following logarithmic Schrodinger equation -Delta u + V(x)u = u log u(2), x is an element of R-N. The classical variational methods cannot... 
EXISTENCE | MATHEMATICS, APPLIED | SOLITARY WAVES | BOUNDARY-VALUE-PROBLEMS | STANDING WAVES | PRINCIPLE | NODAL CHARACTER | PHYSICS, MATHEMATICAL | non-smooth analysis | logarithmic Schrodinger equations | nodal solutions | ORBITAL STABILITY
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2016, Volume 71, Issue 9, pp. 1898 - 1909
We study global solutions of a class of chemotaxis–haptotaxis systems generalizing the prototype in a bounded domain with smooth boundary, , with parameters... 
Logistic source | Global existence | Chemotaxis–haptotaxis | Boundedness | Chemotaxis-haptotaxis | MATHEMATICS, APPLIED | KELLER-SEGEL SYSTEM | CANCER INVASION | CLASSICAL-SOLUTIONS | TISSUE | EQUATIONS | TIME BLOW-UP | Constants | Mathematical models | Computer simulation | Prototypes | Smooth boundaries
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2017, Volume 262, Issue 11, pp. 5497 - 5517
We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler–Poisson system without temperature damping term.... 
Stability | Energy estimate | Large steady-state solution | Global smooth solution | Non-isentropic Euler–Poisson system | SMOOTH SOLUTIONS | HYPERBOLIC SYSTEMS | HYDRODYNAMIC MODEL | SEMICONDUCTORS | MAXWELL EQUATIONS | LIMIT | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | NONCONSTANT EQUILIBRIUM SOLUTIONS | Non-isentropic Euler Poisson system
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 09/2018, Volume 333, pp. 213 - 224
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 12/2017, Volume 27, Issue 14, pp. 2745 - 2780
This paper deals with the Keller-Segel-Navier-Stokes system {n(t) +u .del(n) =Delta(n) - del.(nS(x,n,c). del c), c(t) +u .del(c) =Delta(c) - c+n, u(t)+(u .... 
Navier-Stokes | Chemotaxis | global existence | EXISTENCE | TENSOR-VALUED SENSITIVITY | MATHEMATICS, APPLIED | BOUNDEDNESS | NONLINEAR DIFFUSION | CHEMOTAXIS-FLUID EQUATIONS | ROTATIONAL FLUX | MODELS | CLASSICAL-SOLUTIONS | BLOW-UP | SATURATION
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2019, Volume 47, pp. 484 - 495
In this paper, we are concerned with the problem of periodic solutions for a class of second order periodically forced nonlinear damped Duffing equations with... 
Damping | Discontinuity | Harmonic and subharmonic solutions | Poincaré–Bohl theorem | EXISTENCE | MATHEMATICS, APPLIED | ARCHETYPAL OSCILLATOR | Poincare-Bohl theorem | SMOOTH | Nonlinear equations | Duffing equation | Existence theorems
Journal Article