Keywords: Chaotic system; Fractional differential equation; Local and global stability; Numerical simulations; Relative error; Spatiotemporal oscillations; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
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Keywords: Atangana-Baleanu-Caputo derivative; Fractional reaction-diffusion; Hopf bifurcation; Spatiotemporal system; Oscillations; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10,;
Keywords: Exponential time-integrator; Fractional reaction-diffusion; Nonlinear PDEs; Numerical simulations; Hopf-bifurcation; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Keywords: 35J60; 35J61; 35J75; 35A05; 35R06; Nonlinear elliptic equations; Singular elliptic equations; Uniqueness; Measure data;
Keywords: 35A05; 76A10; 76D03; Compressible viscoelastic fluid; Weak solution; Effective viscous flux; Global well-posedness;
Keywords: 26A33; 35A05; 35A08; Time-space fractional diffusion equation; Mild solution; Existence and uniqueness; Nonnegativity; Mass conservation; Finite time blow up;
Keywords: Caputo derivative; Exponential integrator; Fractional reaction-diffusion; Hopf bifurcation; Oscillations; Predator-prey system; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Keywords: 34A34; 35A05; 35K57; 65L05; 65M06; 93C10; Fourier spectral method; Exponential integrator; Fractional reaction-diffusion; Nonlinear PDEs; Numerical simulations; Spatiotemporal structures;
Keywords: primary; 35B40; 35A05; secondary; 35B35; 85A05; Compressible Navier-Stokes equations; Regular solutions; Vanishing viscosity limit; Vacuum; Degenerate viscosity; Shallow water;
Keywords: 35A05; 35C08; 35Q70; Skew-symmetric Chern-Simons system; Bubbling solutions; Non-degeneracy;
Keywords: 57R35; 35A05; 35A30Global injectivity; Characteristics and global solvability of partial differential equations
Keywords: 35A05; 76A10; 76D03Incompressible elastodynamics; Free boundary; A priori estimates; The second fundamental form
Keywords: 35A05; 35B40; 45C05; 45K05; 82D60; 92D25; 62G05; 62G20Growth-fragmentation; Cell division; Nonparametric estimation; Bias selection; Minimax rates of convergence; Bellman–Harris processes
Keywords: 35A05; 35L72; 45D05; 45G10Nonlinear viscoelastic equations; Memory kernel; Existence of solutions; Uniqueness; Continuous dependence
Keywords: 26A33; 35A05; 35K55; 35S10; 76S05Nonlinear fractional diffusion; Nonlocal diffusion operators; Logarithmic diffusion; Viscous transport equations
Analysis and numerical simulation of multicomponent system with Atangana-Baleanu fractional derivative
Keywords: Mittag-Leffler; Fractional derivative; Hopf-bifurcation; Oscillations; Predator-prey; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations
Keywords: Caputo derivative; Difference methods; Fractional subdiffusion-reaction systems; Pattern formation; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative
Keywords: Caputo-Fabrizio derivative; Fractional Adams-Bashforth method; Error analysis; Nonlinear chaotic systems; Numerical simulations; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
The existence and uniqueness of positive monotone solutions for a class of nonlinear Schrödinger equations on infinite domains
Keywords: 34B18; 35A05; 35J65; Nonlinear Schrödinger equation; Positive solutions; Fixed point; Weighted norm;
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense
Keywords: Caputo-Fabrizio derivative; Exponential decay-law; Exponential time differencing; Finite difference method; Fractional nonlinear PDEs; Numerical simulations; Riemann-Liouville definition; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Global regularity for supercritical nonlinear dissipative wave equations in 3D
Keywords: primary; 35L70; secondary; 35A05; Wave equation; Nonlinear damping; Supercritical; Regularity;
Solutions in H1 of the steady transport equation in a bounded polygon with a fully non-homogeneous velocity
Keywords: 35A05; 35D05; 35D10; 76A05; Transport equation; Nonstandard boundary condition; Localization methods;
Corrigendum to “Smooth zero-contact-angle solutions to a thin-film equation around the steady state” [J. Differential Equations 245 (2008) 1454–1506]
Keywords: 35A05; 35K65; 35Q35; 35R35; 76A20; 76D08; 76D27Existence and uniqueness; Fourth order degenerate parabolic equations; Thin-film equations; Free boundary problems; Lubrication theory; Hele-Shaw flow
On the nonlinear scattering and well-posedness for a 2D-Boussinesq–Benney–Luke type system
Keywords: 35Q35; 35A05; 35B40Local and global well-posedness; Nonlinear scattering
A note on the Camassa-Holm equation
Keywords: 35G25; 35L05; 35A05; Hyperelastic-rod wave equation; Camassa-Holm equation; Weak solutions; Existence; Compactness;
Dynamics of the 3-D fractional complex Ginzburg–Landau equation
Keywords: 35A05; 35B40; 35B45Fractional Ginzburg–Landau equation; Global smooth solution; Global attractor; Hausdorff dimension; Fractal dimension
Kato-type estimates for NLS equation in a scalar field and unique solvability of NKGS system in energy space
Keywords: 35A05; 35E10; 35G25; 35L70; 81Q05Kato-type estimates; Schrödinger equation; Unique solvability; Klein–Gordon–Schrödinger equations
Combined effects in nonlinear problems arising in the study of anisotropic continuous media
Keywords: 35A05; 35B40; 35J60; 58E05Lane–Emden–Fowler equation; Bifurcation problem; Anisotropic continuous media; Perturbation; Positive solution
Relatively optimal filtering on a Hilbert space for measure driven stochastic systems
Keywords: 34G20; 34K30; 35A05; 35B30; 93C25Linear filtering; Hilbert space; Signed measures; Impulsive systems; Measure driven differential Riccati equation; C0C0-semigroups
On radially symmetric solutions of the compressible isentropic self-gravitating fluid
Keywords: 35A05; 76N10Navier–Stokes equations; Cauchy problem; Weak solution; Strong solution; Radially symmetric; Uniqueness; Self-gravitating fluid
Perturbation effects in nonlinear eigenvalue problems
Keywords: 35A05; 35B40; 35J60; 37K50; 92D25Logistic equation; Nonlinear eigenvalue problem; Positive entire solution; Spectrum; Anisotropic potential; Perturbation; Population dynamics
Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations
Keywords: 49L25; 35F25; 35K65; 35A05; 35D05; 45G10; 47H10Nonlocal Hamilton–Jacobi Equations; Existence results; Dislocation dynamics; Fitzhugh–Nagumo system; Nonlocal front propagation; Viscosity solutions; L1L1-dependence in time
Optimality conditions with state constraints for semilinear systems determined by operator valued measures
Keywords: 35K10; 35L10; 34G20; 34K30; 35A05; 93C20Evolution equations; Operator valued measures; Vector measures; Optimal control; Necessary conditions of optimality
Global weak solutions and wave breaking phenomena to the periodic Degasperis–Procesi equation with strong dispersion
Keywords: 35A05; 35B10; 35D05; 35E15; 35G25Degasperis–Procesi equation; Global weak solution; Breaking waves; Peakon; Shockpeakon
Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data
Keywords: 35J70; 35D05; 35A05; 46E35Elliptic equation; Variable exponents; Renormalized solution; Existence; Uniqueness
Parabolic systems determined by strongly nonlinear operator-valued measures
Keywords: 35K10; 35L10; 34G20; 34K30; 35A05; 93C20Strongly nonlinear operator-valued measures; Existence of solutions; Regularity properties
Global existence and causality for a hyperbolic transmission problem with a repulsive nonlinearity
Keywords: 35A05; 35C15; 35E15; 35L70; 35L90; 42A38; Transmission problem; Klein-Gordon equation; Repulsive nonlinearity; Global existence; Energy estimates; Causality;
Evolution equations determined by operator valued measures and optimal control
Keywords: 34G20; 34K30; 35A05; 93C25Differential inclusions; Banach spaces; Operator valued measures; Hybrid systems; Existence of solutions; Optimal control
On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation
Keywords: 35G25; 35L05; 35A05; 35L65Shallow water equation; Integrable equation; Hyperbolic equation; Discontinuous solution; Weak solution; Entropy condition; Existence; Uniqueness
Some new nonlinear inequalities and applications to boundary value problems
Keywords: 26D10; 26D20; 35A05; 35B05; 35B30; 35B35; Retarded Gronwall-Bellman-Ou-Iang type inequalities; Boundary value problems; Boundedness; Uniqueness; Continuous dependence;
Some nonlinear equations of the nonstable filtration type and embedding theorems
Keywords: primary; 35J65; 35K60; 35A05; secondary; 46G15Elliptic–parabolic equation; Degeneracy; Nonlinear mixed problem; Sobolev and pn-space; Embedding theorem; Solvability theorem
Measure-valued solutions for a hierarchically size-structured population
Keywords: 35A05; 35D05; 35F25; 35L67; 92D25; Hierarchical size-structured population model; Measure-valued solutions; Viscosity method; Growth rate with an Allee effect;