Formulation and Analysis of a Parabolic Transmission Problem on Disjoint Intervals
Fully Discrete Galerkin Approximations of Parabolic Boundary-Value Problems with Nonsmooth Boundary Data.
Fundamental solution of initial-boundary value problem for fourth-order pseudoparabolic equations with nonsmooth coefficients.
Galerkin approximations to non-linear pseudo-parabolic partial differential equations. (Short Communication).
Galerkin approximations to non-linear pseudo-parabolic partial differential equations.
Gevrey problem for parabolic equations with changing time direction.
Global regular solutions to the Navier-Stokes equations in a cylinder
The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder Ω and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to and the gradient of the pressure to . We prove the existence of solutions without any restrictions on the lengths of the...
Gradient estimates in parabolic problems with unbounded coefficients
We study, with purely analytic tools, existence, uniqueness and gradient estimates of the solutions to the Neumann problems associated with a second order elliptic operator with unbounded coefficients in spaces of continuous functions in an unbounded open set Ω in .
Grandient Estimates for Degenerate Diffusion Equations. I.
Green function for the heat equation with oblique boundary conditions in an angle
Group method analysis of two-dimensional plate in heat flux.
Hamilton-Jacobi equations for control problems of parabolic equations
We study Hamilton-Jacobi equations related to the boundary (or internal) control of semilinear parabolic equations, including the case of a control acting in a nonlinear boundary condition, or the case of a nonlinearity of Burgers' type in 2D. To deal with a control acting in a boundary condition a fractional power – where (A,D(A)) is an unbounded operator in a Hilbert space X – is contained in the Hamiltonian functional appearing in the Hamilton-Jacobi equation. This situation has already...
Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term.
Heat distribution in a medium with concentrated perturbation of density.
Heat flow, brownian motion and newtonian capacity
Heat Flow out of Regions in IRm.
Heteroclinic connections of stationary solutions of scalar reaction-diffusion equations