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SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 5, pp. 3993 - 4024
This paper is concerned with the limiting behavior of coexistence steady states of the Lotka-Volterra competition model as a cross-diffusion term tends to... 
Blow up | Bifurcation | A priori estimate | Cross-diffusion | Nonlinear elliptic system | Asymptotic behavior | MATHEMATICS, APPLIED | STEADY-STATES | POSITIVE SOLUTIONS | STABILITY | blow up | nonlinear elliptic system | LOTKA-VOLTERRA COMPETITION | POPULATION-MODELS | bifurcation | asymptotic behavior | SPATIAL SEGREGATION | SYSTEMS | a priori estimate | cross-diffusion
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2017, Volume 56, Issue 4, pp. 1 - 28
Cui and Lou (J Differ Equ 261:3305–3343, 2016) proposed a reaction–diffusion–advection SIS epidemic model in heterogeneous environments, and derived... 
92D25 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B32 | Mathematics | 35K57 | 35J55 | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTIC PROFILES | TRANSMISSION | PERIODIC ENVIRONMENT | DYNAMICS | POSITIVE STEADY-STATE | RISK | Epidemics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2004, Volume 197, Issue 2, pp. 293 - 314
This paper is concerned with a cross-diffusion system arising in a prey–predator population model. The main purpose is to discuss the stability analysis for... 
Cross diffusion | Steady-state solution | Stability | Hopf bifurcation | Lyapunov–Schmidt reduction | Lyapunov-Schmidt reduction | MATHEMATICS | HOPF-BIFURCATION | EQUATIONS | cross diffusion | PRINCIPLE | steady-state solution | stability
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 2009, Volume 10, Issue 2, pp. 943 - 965
This paper is concerned with the following Lotka–Volterra cross-diffusion system in a spatially heterogeneous environment (SP) { Δ [ ( 1 + k ρ ( x ) v ) u ] +... 
Cross-diffusion | Lyapunov–Schmidt reduction | Bifurcation | Multiple coexistence states | Perturbation | Limiting system | Heterogeneous environment | Lyapunov-Schmidt reduction | MATHEMATICS, APPLIED | STEADY-STATES | STABILITY | PREY-PREDATOR SYSTEM | PATTERNS | DEGENERACY | COMPETITION MODEL
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2018, Volume 44, pp. 589 - 615
This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch... 
Attractive transitional flux | A priori estimate | Prey–predator model | Coexistence steady states | Bifurcation analysis | Asymptotic behavior | MATHEMATICS, APPLIED | GLOBAL BIFURCATION | DIFFERENTIAL-EQUATIONS | ELLIPTIC-SYSTEMS | DIFFUSION | Prey-predator model | PAIRS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2018, Volume 264, Issue 9, pp. 5928 - 5949
We consider the Neumann problem of a 1D stationary Allen–Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric... 
Bifurcation | Level set analysis | Nonlocal term | Monotonicity | Allen–Cahn equation
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2015, Volume 258, Issue 5, pp. 1801 - 1858
This paper is concerned with the Neumann problem of a stationary Lotka-Volterra competition model with diffusion and advection. First we obtain some sufficient... 
Bifurcation | Nonlocal constraint | Degree | Singular perturbation | Reaction-diffusion-advection system | Levelset analysis | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | DISPERSAL | MATHEMATICS | COEXISTENCE | EVOLUTION | CROSS-DIFFUSION | SPATIAL SEGREGATION | SPECIES MODEL | SYSTEMS
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 10/2012, Volume 241, Issue 19, pp. 1629 - 1639
Mimura and one of the authors (1996) proposed a mathematical model for the pattern dynamics of aggregating regions of biological individuals possessing the... 
Bifurcation | Pattern formation | Chemotaxis | SYSTEM | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | BOUNDEDNESS | ATTRACTOR | HEXAGONAL PATTERNS | PHYSICS, MATHEMATICAL | LOGISTIC SOURCE | BLOW-UP | Employee motivation | Analysis | Models
Journal Article
Advances in Differential Equations, ISSN 1079-9389, 2007, Volume 12, Issue 2, pp. 145 - 172
Journal Article
Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 2013, pp. 467 - 476
Journal Article
Discrete and Continuous Dynamical Systems, ISSN 1078-0947, 06/2009, Volume 24, Issue 2, pp. 489 - 509
This paper is concerned with the following Lotka-Volterra cross-diffusion system ut = Delta[(1 + k rho(x)v)u] + u(a - u - c(x)v) in Omega x (0, infinity), tau... 
Stability | Coexistence states | Lyapunov-schmidt reduction | Skt model | Hopf bifurcation | Limiting system | Heterogeneous environment | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | Lyapunov-Schmidt reduction | CROSS-DIFFUSION | SKT model | PREY-PREDATOR SYSTEM | heterogeneous environment | coexistence states | limiting system | stability
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2017, Volume 263, Issue 5, pp. 2687 - 2714
This paper studies the Neumann problem of a nonlocal Allen–Cahn equation in an interval. A main result finds a symmetry breaking (secondary) bifurcation point... 
Bifurcation | Complete elliptic integrals | Nonlocal term | Allen–Cahn equation | Symmetry breaking | MATHEMATICS | EIGENVALUES | Allen-Cahn equation | CELL POLARIZATION | DIFFUSION | MODEL | Analysis | Numerical analysis
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2004, Volume 197, Issue 2, pp. 315 - 348
We study the multiple existence of positive solutions for the following strongly coupled elliptic system: Δ[(1+αv)u]+u(a−u−cv)=0 in Ω, Δ[(1+βu)v]+v(b+du−v)=0... 
Bifurcation | Cross-diffusion | Steady state | Lyapunov–Schmidt reduction | Lyapunov-Schmidt reduction | steady state | MATHEMATICS | bifurcation | STEADY-STATES | MODELS | POSITIVE SOLUTIONS | STABILITY | DIFFERENTIAL-EQUATIONS | cross-diffusion | UNIQUENESS | PAIRS
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 10/2016, Volume 36, Issue 10, pp. 5627 - 5655
We show existence, nonexistence, and exact multiplicity for stationary limiting problems of a cell polarization model proposed by Y. Mori, A. Jilkine and L.... 
Bifurcation | Level set analysis | Nonlocal term | Elliptic integral | Reaction diffusion model | Exact solution | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | bifurcation | exact solution | PATTERNS | level set analysis | DIFFUSION | nonlocal term | elliptic integral
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 323, Issue 2, pp. 1387 - 1401
Journal Article
Japan Journal of Industrial and Applied Mathematics, ISSN 0916-7005, 7/2018, Volume 35, Issue 2, pp. 441 - 475
From the viewpoint of pattern formation, Keller–Segel systems with growth terms are studied. These models exhibit various stationary and spatio-temporal... 
70K50 | Pattern formation | Computational Mathematics and Numerical Analysis | 35B36 | 92C15 | Shadow system | Bifurcation analysis | 35B32 | Mathematics | Applications of Mathematics | Keller–Segel system with growth | 35Q92 | PATTERN-FORMATION | TISSUE INFLAMMATION | MATHEMATICS, APPLIED | STABILITY | EQUATIONS | DIFFUSION | MODEL | ATTRACTOR | Keller-Segel system with growth
Journal Article
Nonlinearity, ISSN 0951-7715, 05/2013, Volume 26, Issue 5, pp. 1313 - 1343
This paper is concerned with stationary solutions of a reaction-diffusion-advection system arising in surface chemistry. Hildebrand et al (2003 New J. Phys. 5... 
MATHEMATICS, APPLIED | BOUNDARY | PHYSICS, MATHEMATICAL | BIFURCATION | Shadows | Infinity | Singular perturbation | Spots | Surface chemistry | Bifurcations | Mathematical models | Constraining
Journal Article
Nonlinear Analysis. Real World Applications, ISSN 1468-1218, 12/2018, Volume 44, p. 589
This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch... 
Nonlinear equations | Asymptotic properties | Flux | Bifurcations | Mathematical models | Predation | Asymptotic methods | Population density
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 12, pp. e2223 - e2232
We study a prey–predator model with nonlinear diffusions. In a case when the spatial dimension is less than 5, a universal bound for coexistence steady-states... 
Bifurcation | Cross-diffusion | A priori estimate | Nonlinear diffusion of fractional type | Coexistence steady-states | MATHEMATICS | MATHEMATICS, APPLIED | Nonlinearity | Bifurcation theory | Mathematical models | Diffusion | Continuums
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 11/2012, Volume 17, Issue 8, pp. 2745 - 2769
This paper deals with the following reaction-diffusion system (SP) {Delta[(1 + alpha nu)u] + u(a - u - cv) = 0 Delta[(1 + beta u)v] + v(b - du - v) = 0 in a... 
Bifurcation | Limit system | Cross-diffusion | Population model | A priori estimates | Positive solution | MATHEMATICS, APPLIED | STEADY-STATES | POSITIVE SOLUTIONS | EQUATIONS | LOTKA-VOLTERRA COMPETITION | a priori estimates | bifurcation | positive solution | limit system | SPATIAL SEGREGATION | population model | DOMAINS | cross-diffusion
Journal Article
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