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Using meshes defined by the nodal hierarchy, an edge based multigrid hierarchy is developed, which includes inter-grid transfer operators, coarse grid discretizations, and coarse

In section 2 we present the model in its original form and establish an equivalent formulation using boundary integrals. This is then used to devise a semi-implicit algorithm

Theorem 4.8 shows that the addition of the nonlocal term to local diffusion pro- duces similar early pattern results when compared to the pure local case considered in [33].. Lemma

Kilbas; Conditions of the existence of a classical solution of a Cauchy type problem for the diffusion equation with the Riemann-Liouville partial derivative, Differential Equations,

Turmetov; On solvability of a boundary value problem for a nonhomogeneous biharmonic equation with a boundary operator of a fractional order, Acta Mathematica Scientia.. Bjorstad;

The study of the eigenvalue problem when the nonlinear term is placed in the equation, that is when one considers a quasilinear problem of the form −∆ p u = λ|u| p−2 u with

Key words and phrases: Optimal lower bound, infimum spectrum Schr˝odinger operator, Sobolev inequality.. 2000 Mathematics

In our model we take into account only diffusion and velocity of chemical reaction near the surface of the crystal and suggest applying non-linear reaction-diffusion equation with