Note on the stability of the Dirichlet problem and the Poisson equation
Note on two compatibility criteria: Jacobi-Mayer bracket vs. differential Gröbner basis.
Numerical and theoretical treating of evolution problems by the method of discretization in time
Numerical blow-up solutions for some semilinear heat equations.
Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions.
Numerical calculation of singularities for Ginzburg-Landau functionals.
Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint
We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint
We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
Numerical methods for solving variational inequalities
Numerical solution for nonlocal Sobolev-type differential equations.
Numerical solutions to integral equations equivalent to differential equations with fractional time
This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
Numerical studies of groundwater flow problems with a singularity
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...
Oddness of least energy nodal solutions on radial domains.
On a class of elliptic differential operators degenerating at one point
On a class of variational-hemivariational inequalities.
On a coupled problem between the plate equation and the membrane equation on polygons
On a generalized Stokes problem
We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.
On a Global Existence Theorem of Small Amplitude Solutions for Nonlinear Wave Equations in an Exterior Domain.
On a holomorphic solution of a singular partial differential equation with many simple poles
On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values
We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values with By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case of (P) in which the nonlinear term contains the sum . Under suitable conditions, we prove that the solution of converges to the solution of the corresponding...