The Dirac Equation with an Anomalous Magnetic Moment.
The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion
In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spatial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem is established...
The Dirichlet boundary value problem for the system uxi-xj=0, j≠i.
The Dirichlet problem for elliptic equations in the plane
In this paper an existence and uniqueness theorem for the Dirichlet problem in for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class VMO.
The Dirichlet problem for the Monge-Ampère equation in convex (but not strictly convex) domains.
The Dirichlet problem in half-space for elliptic equations with unbounded coefficients
The discontinuous boundary problem for transversally-isotopic plates containing linear defects.
The dyadic fractional diffusion kernel as a central limit
We obtain the fundamental solution kernel of dyadic diffusions in as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.
The evolution dam problem for nonlinear Darcy's law and Dirichlet boundary conditions.
The existence and the continuation of holomorphic solutions for convolution equations in tube domains
The existence of Carathéodory solutions of hyperbolic functional differential equations
We consider the following Darboux problem for the functional differential equation a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]where the function is defined by for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.
The finite integral transform method for a parabolic differential equation on a graph.
The first boundary value problem for the vibrating string equation in domains with piecewise smooth boundary
The first eigenvalue for the -Laplacian operator.
The Gauss center research in multiscale scientific computation.
The generalized Burgers equation with and without a time delay.
The Ginzburg-Landau equations of superconductivity and the one-phase Stefan problem
The heat transform and its use in thermal identification problems for electronic circuits.
The Hopf bifurcation theorem for parabolic equations with infinite delay
The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
The H-theorem for Boltzmann type equations.