Communications on Pure and Applied Analysis
August 2022 , Volume 21 , Issue 8
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We are concerned with sign-changing solutions and their concentration behaviors of singularly perturbed Kirchhoff problem
This paper is concerned with the pathwise dynamics of stochastic fractional lattice systems driven by Wong-Zakai type approximation noises. The existence and uniqueness of pullback random attractor are established for the approximate system with a wide class of nonlinear diffusion term. For system with linear multiplicative noise and additive white noise, the upper semicontinuity of random attractors for the corresponding approximate system are also proved when the step size of the approximation approaches zero.
We prove multiplicity results for solutions, both with positive and negative energy, for a class of singular quasilinear Schrödinger equations in the entire
We present a weighted
We consider the initial value problem (IVP) associated to a coupled system of modified Kawahara/KdV type equations with polynomials nonlinearities. For the model in question, the Cauchy problem is of interest, and is shown to be well-posed for given data in a Gevrey spaces. Our results make use of techniques presented in Grujić and Kalisch, who studied the Gevrey regularity for a class of water-wave models and the well-posedness of a IVP associated to a general equation. The proof relies on estimates in space-time norms adapted to the linear part of the equations. In particular, estimates in Bourgain spaces are proven for the linear and nonlinear terms of the system and the main result is obtained by a contraction principle. The class of system in view generalizes the system of modified Kawahara/KdV type equations studied by Kondo and Pes, which contains a number of systems arising in the modeling of waves in fluids, stability and instability of solitary waves and models for wave propagation in physical systems where both nonlinear and dispersive effects are important.
In this paper, we analyze a nonlinear equation modeling the mechanical replication of the DNA molecule based on a Kolmogorov-Jhonson-Mehl-Avrami (KJMA) type model inspired on the mathematical analogy between the DNA replication process and the crystal growth. There are two different regions on the DNA molecule deep into a duplication process, the connected regions where the base pairs have been already duplicated, called eyes or islands and the regions not yet duplicated, called holes. The Cauchy problem associated with this model will be analyzed, where some dependences and nonlinearities on the replication velocity and the origins of replication are introduced.
Rencently Chow, Huang, Li and Zhou proposed discrete forms of the Fokker-Planck equations on a finite graph. As a primary step, they constructed Riemann metrics on the graph by endowing it with some kinds of weight. In this paper, we reveal the relation between these Riemann metrics and the Euclidean metric, by showing that they are locally equivalent. Moreover, various Riemann metrics have this property provided the corresponding weight satisfies a bounded condition. Based on this, we prove that the two-side Łojasiewicz inequality holds near the Gibbs distribution with Łojasiewicz exponent
We study the existence of the solution to a semilinear higher-order elliptic system
with the homogeneous Dirichlet boundary conditions. Here,
In this paper, we consider the multiplicity of nodal solutions for the following Kirchhoff type equations:
Using a Lyapunov-Krasovskii functional, new results concerning the global stability, boundedness of solutions, existence and non-existence of
In this paper we explore the theory of fractional powers of positive operators, more precisely, we use the Balakrishnan formula to obtain parabolic approximations of (damped) wave equations in bounded smooth domains in
Considered herein is the initial boundary value problem associated with a sixth-order nonlinear parabolic equation in a bounded domain. We first establish a new global Carleman estimate for the sixth-order parabolic operator. Based on this estimate, we obtain the local exact controllability to the trajectories and the unique continuation property of the parabolic equation.
In this paper, we are concerned with the uniqueness result for non-negative solutions of the higher-order Lane-Emden equations involving the GJMS operators on
In this paper we investigate the existence and the properties for the minimisers of a special Helfrich functional for surfaces of revolution with Dirichlet boundary value conditions. Removing the even restriction for the admissible functions in [
We study the fractional Cucker-Smale (in short, CS) model under general network topologies. In [
In this paper, we study the following high-order Hardy-H
Then by using the method of moving planes in integral forms, we prove that there are no positive solutions for the above integral system. In addition, while in the subcritical case
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