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Global solutions in the critical Sobolev space for the Landau equation
The Landau equation is studied for hard potential with −2 ≤ γ ≤ 1. Under a perturbation setting, a unique global solution of the Cauchy problem to...
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Fast Parallel Solver of Time-harmonic Wave Equation with Topography
AbstractDesigning a fast solver for the time-harmonic wave equation is a well-known challenging problem. However, when variable land and/or marine...
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Dynamic Programming of the Stochastic Burgers Equation Driven by Lévy Noise
In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Lévy-type noises with distributed control process...
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Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations
The aim of this paper is to propose a new method to construct pullback exponential attractors with explicit fractal dimensions for non-autonomous...
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Three-Dimensional Elements
This chapter starts with the analytical description of solid or three-dimensional members. Based on the three basic equations of continuum mechanics,...
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Efficient Method for Solving the Boltzmann Equation on a Uniform Mesh
AbstractA new numerical method for solving the Boltzmann equation on a uniform mesh in velocity space is proposed. The asymptotic complexity of the...
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Well-posedness and finite element approximation of mixed dimensional partial differential equations
In this article, a mixed dimensional elliptic partial differential equation is considered, posed in a bulk domain with a large number of embedded...
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Averaging Principle for Two Time-Scales Stochastic Partial Differential Equations with Reflection
In this work, we consider a system of fast and slow time-scale stochastic partial differential equations with reflection, where the slow component is...
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New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations
This paper is devoted to obtaining new lower bounds to the radius of spatial analyticity for the solutions of modified Korteweg–de Vries (mKdV)...
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Sixth-order compact difference scheme and multigrid method for solving the Poisson equation
This paper proposes a sixth-order compact difference scheme of Poisson equation based on the sixth-order compact difference operator of the second...
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Some Results for a von Kármán Equation with Variable Exponent Modeling Suspension Bridges
A von Kármán equation with variable exponent is considered. The equation with partial free boundary conditions can be viewed as a mathematical model...
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Differential Graded Lie Algebras
In this chapter we introduce the basic algebraic theory of differential graded vector spaces and differential graded Lie algebras over an arbitrary...
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New Family of Solitary Wave Solutions to New Generalized Bogoyavlensky–Konopelchenko Equation in Fluid Mechanics
Many mathematicians and physicists are interested in Bogoyavlensky–Konopelchenko type equations to illustrate the various dynamics of nonlinear wave...
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The analytic smoothing effect of solutions for the nonlinear spatially homogeneous Landau equation with hard potentials
In this work, we study the Cauchy problem of the nonlinear spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium...
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A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes
In this paper, we present a divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes. The velocity and the...
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On an accurate numerical integration for the triangular and tetrahedral spectral finite elements
In the triangular/tetrahedral spectral finite elements, we apply a bilinear/trilinear transformation to map a reference square/cube to a...