A Discrete Sampling Inversion Scheme for the Heat Equation.
A double complex related with a system of partial differential equations. II
A double complex related with a system of partial differential equations. I
A FETI-DP preconditioner for mortar methods in three dimensions.
A finite difference approach for the initial-boundary value problem of the fractional Klein-Kramers equation in phase space
Considering the features of the fractional Klein-Kramers equation (FKKE) in phase space, only the unilateral boundary condition in position direction is needed, which is different from the bilateral boundary conditions in [Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers...
A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition
We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear...
A finite element solution of the monlinear heat equation
A finiteness result in the free boundary value problem for minimal surfaces
A free boundary problem arising in magnetohydrodynamic system
A free boundary problem describing the saturated-unsaturated flow in a porous medium. II: Existence of the free boundary in the 3D case.
A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor
A free boundary problem for a predator-prey model with nonlinear prey-taxis
This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary...
A free boundary problem for quasi-linear elliptic equations
A free boundary problem for semilinear elliptic equations.
A free boundary problem for some modified predator-prey model in a higher dimensional environment
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as goes to infinity and survives in the new environment, or it fails to establish...
A free boundary problem for the -Laplacian: uniqueness, convexity, and successive approximation of solutions.
A free boundary problem involving limiting Sobolev exponents.
A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process
We investigate the behaviour of the meniscus of a drop of liquid aluminium in the neighbourhood of a state of equilibrium under the influence of weak electromagnetic forces. The mathematical model comprises both Maxwell and Navier-Stokes equations in 2D. The meniscus is governed by the Young-Laplace equation, the data being the jump of the normal stress. To show the existence and uniqueness of the solution we use the classical implicit function theorem. Moreover, the differentiability of the operator...
A frictional contact problem with wear and damage for electro-viscoelastic materials
We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational...
A general analytical result for non-linear SPDE's and applications.