Communications on Pure & Applied Analysis
July 2019 , Volume 18 , Issue 4
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We consider a stress-energy tensor describing a pure radiation viscous fluid with conformal symmetry introduced in [
In this paper, we obtain the interior gradient estimate of some nonlinear equations which arise naturally from prescribed curvature problem of graphs in hyperbolic space. The method depends on the maximum principle.
This paper is concerned with the asymptotic dynamics of two species competition systems of the form
This paper is concerned with the following memory-type Bresse system
with homogeneous Dirichlet-Neumann-Neumann boundary conditions, where
Under appropriate conditions on
We consider the existence of positive solutions for the following fractional Schrödinger-Poisson system
Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of
We consider the Dirac equations with cubic Hartree-type nonlinearity which are derived by uncoupling the Dirac-Klein-Gordon systems. We prove small data global well-posedness and scattering results in the full scaling subcritical regularity regime. The strategy of the proof relies on the localized Strichartz estimates and bilinear estimates in
We give an alternative proof of the global existence result originally due to Hidano and Yokoyama for the Cauchy problem for a system of quasi-linear wave equations in three space dimensions satisfying the weak null condition. The feature of the new proof lies in that it never uses the Lorentz boost operator in the energy integral argument. The proof presented here has an advantage over the former one in that the assumption of compactness of the support of data can be eliminated and the amount of regularity of data can be lowered in a straightforward manner. A recent result of Zha for the scalar unknowns is also refined.
We study the Boltzmann equation near a global Maxwellian. We prove the global existence of a unique mild solution with initial data which belong to the
We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived in [
The existence of the uniform global attractor for a second order non-autonomous lattice dynamical system (LDS) with almost periodic symbols has been carefully studied. Considering the nonlinear operators
In this paper we study an equation driven by a nonlocal anisotropic operator with homogeneous Dirichlet boundary conditions. We find at least three non trivial solutions: one positive, one negative and one of unknown sign, using variational methods and Morse theory. We present some results about regularity of solutions such as
This paper is concerned with long-time dynamics of binary mixture problem of solids, focusing on the interplay between nonlinear damping and source terms. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that such unique solutions depend continuously on the initial data. We also establish the existence of a global attractor, and we study the fractal dimension and exponential attractors.
In this paper, we establish the local well-posedness of low regularity solutions to the general second order strictly hyperbolic equation of divergence form
We consider the following singularly perturbed problem
Existence of a solution with a spike layer near a min-max critical point of the mean curvature on the boundary
We study the Cauchy problem of the damped wave equation
and give sharp
In this work we consider the following class of fractional
We consider the chemotaxis-haptotaxis system
in a bounded convex domain
It is asserted that whenever
the Neumann boundary problem with suitably regular initial data possesses a unique global and bounded classical solution.
In this paper, we consider the multidimensional stability of planar traveling waves for the nonlocal dispersal competitive Lotka-Volterra system with time delay in
We study analytically and numerically the existence and orbital stability of the peak-standing-wave solutions for the cubic-quintic nonlinear Schródinger equation with a point interaction determined by the delta of Dirac. We study the cases of attractive-attractive and attractive-repulsive nonlinearities and we recover some results in the literature. Via a perturbation method and continuation argument we determine the Morse index of some specific self-adjoint operators that arise in the stability study. Orbital instability implications from a spectral instability result are established. In the case of an attractive-attractive case and an focusing interaction we give an approach based in the extension theory of symmetric operators for determining the Morse index.
A formula for smooth orbiforms originating from Euler can be adjusted to describe all sets of constant width in 2d. Moreover, the formula allows short proofs of some laborious approximation results for sets of constant width.
In this paper, we study the large time behaviors of boundary layer solution of the inflow problem on the half space for a class of isentropic compressible non-Newtonian fluids. We establish the existence and uniqueness of the boundary layer solution to the non-Newtonian fluids. Especially, it is shown that such a boundary layer solution have a maximal interval of existence. Then we prove that if the strength of the boundary layer solution and the initial perturbation are suitably small, the unique global solution in time to the non-Newtonian fluids exists and asymptotically tends toward the boundary layer solution. The proof is given by the elementary energy method.
We present an analysis based on word combinatorics of splitting integrators for Ito or Stratonovich systems of stochastic differential equations. In particular we present a technique to write down systematically the expansion of the local error; this makes it possible to easily formulate the conditions that guarantee that a given integrator achieves a prescribed strong or weak order. This approach bypasses the need to use the Baker-Campbell-Hausdorff (BCH) formula and shows the existence of an order barrier of two for the attainable weak order. The paper also provides a succinct introduction to the combinatorics of words.
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