Showing papers in "Journal of Differential Equations in 2018"

TL;DR: In this article, a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations are analyzed, based on the Hirota bilinear formulation and the primary object is the class of positive multivariate quadrastic functions.

TL;DR: In this article, the authors obtained various existence and multiplicity results for the following double phase problem by variational method, including a sign-changing ground state solution and some properties of double phase operator.

TL;DR: In this article, the authors studied the question of whether a forced moving KPP nonlinearity from behind can give rise to traveling waves with the same speed and how they attract solutions of initial value problems when they exist.

TL;DR: It is shown that the attractors of Wong–Zakai approximations converges to the attractor of the stochastic reaction–diffusion equation for both additive and multiplicative noise.

TL;DR: In this article, the authors considered the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales and showed that the slow component strongly converges to the solution of the corresponding averaged equation under some suitable conditions.

TL;DR: In this paper, an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory was developed for the construction of global bounded weak solutions to an associated initial-boundary value problem under the assumption that (0.1) m > 9 8.

TL;DR: In this paper, a generalized Keller-Segel equation for nonlinear fractional time-space generalized Cauchy problems was investigated and the existence and uniqueness of the mild solutions were established when the initial data are in L p spaces or the weighted spaces.

TL;DR: In this paper, the authors investigated the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction diffusion equations in H s ( R n ) with s ∈ ( 0, 1 ).

TL;DR: In this article, the authors investigated a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts and proved that the solution of the model exists globally and the model system possesses a global attractor.

TL;DR: In this paper, the existence of a globally defined pair ( u, v ) of radially symmetric functions which are continuous in ( Ω ¯ ∖ { 0 } ) × [ 0, ∞ ) and smooth in ( ǫ¯ ∖ [ 0 } ] × ( 0, ∞ ), and which solve the corresponding initial-boundary value problem for (⋆) with ( u ( ⋅, 0 ), v, v ) = ( u 0, v 0 ) in an appropriate generalized sense.

TL;DR: In this paper, an initial boundary value problem for a fractional diffusion equation on ( 0, T ) × M, T > 0, with time-fractional Caputo derivative of order α ∈ ( 0, 1 ) ∪ ( 1, 2 ).

TL;DR: In this paper, the authors studied the smoothness of Hopf bifurcation at a fine focus or a center, and of Poincare bifurbcation in a period annulus.

TL;DR: In this paper, the authors study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries and investigate the existence and uniqueness, regularity and uniform estimates, and long time behaviors of global solution.

TL;DR: In this article, the authors studied the nonlinear Schrodinger equation with an inverse-square potential in dimensions 3 ≤ d ≤ 6 and considered both focusing and defocusing nonlinearities in the mass supercritical and energy subcritical regime.

TL;DR: In this paper, the existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by − Δ u = h ( u ) f in Ω, where f is an irregular datum, possibly a measure, and h is a continuous function that may blow up at zero.

TL;DR: In this article, the authors investigated the stability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation when the given parameter of the model is near the principle eigenvalue of an elliptic operator.

TL;DR: In this article, the rough path counterpart of Ito stochastic integration and differential equations driven by general semimartingales was developed, which significantly enlarges the classes of (Ito/forward) stochastically differential equations treatable with pathwise methods.

TL;DR: In this article, the authors present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations, based on maximal L p -regularity in time-weighted function spaces.

TL;DR: In this article, the initial value problem for the Sasa-Satsuma equation is transformed to a 3 × 3 matrix Riemann-Hilbert problem with the help of the corresponding Lax pair.

TL;DR: In this paper, the authors prove the existence of renormalized solutions to general nonlinear elliptic equation in Musielak-Orlicz space avoiding growth restrictions without any particular type of growth condition of M or its conjugate M ⁎.

TL;DR: In this paper, the authors analyzed the long-time behavior of the solution of the initial value problem (IVP) for the short pulse (SP) equation, which posses a Wadati-Konno-Ichikawa (WKI)-type Lax pair.

TL;DR: In this paper, the singular case 0 β 1 was considered and it was shown that extremal functions for these singular inequalities exist for all τ > 0, 0 β1 and 0 γ ≤ 1 − β. The proof is based on blowup analysis.

TL;DR: In this article, the authors focus their attention on the following nonlinear fractional Schrodinger equation with magnetic field e 2 s ( − Δ ) A / e s u + V ( x ) u = f ( | u | 2 ) u ǫ in R N, where e > 0 is a parameter, s ∈ ( 0, 1 ), N ≥ 3, ( − ε ) A s is the fractional magnetic Laplacian, V : R N → R and A : R n → R N are continuous potentials and f

TL;DR: In this article, the authors considered the fractional order static Hartree equations with critical nonlocal nonlinearity and proved that the positive solutions are radially symmetric about some point in R d and must assume the certain explicit forms.

TL;DR: In this paper, a two-competing-species chemotaxis system with consumption of chemoattractant was considered, and the authors proved asymptotic stabilization of solutions in the sense that the corresponding initial-boundary value problem possesses a unique global bounded classical solution.

TL;DR: In this paper, the authors studied a more general situation, where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard Dirichlet, Neumann and Robin type conditions as special cases.

TL;DR: In this article, a diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed, and the nonlocal competition strength is determined by a diffusion kernel function to model the movement pattern of the biological species.

TL;DR: In this paper, the authors studied the positive solutions to the singular and non local elliptic problem posed in a bounded and smooth domain and proved the existence of a global multiplicity result for a certain class of nonlinearities f.

TL;DR: In this paper, the authors investigated the existence and asymptotic behavior of nodal solutions to the nonlinear Schrodinger equation and proved that for any positive integer k, the problem has a sign-changing solution u λ k which changes sign exactly k times.

TL;DR: In this paper, it was shown that at free boundary points of positive parabolic density, the time derivative of the solution is Holder continuous and space-time regularity of the corresponding free boundary is obtained for any fraction s ∈ ( 0, 1 ).