Some remarks on the local class field theory of Serre and Hazewinkel
We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.
Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
Mathematical models of tumor growth systems
We study a class of parabolic-ODE systems modeling tumor growth, its mathematical modeling and the global in time existence of the solution obtained by the method of Lyapunov functions.
A Remark on the L... Bounds of the Ritz Operator Associated with a Finite Element Approximation.
Spectral and related properties about the Emden-Fowler equation -...u = ...e... on circular domains.
Self-similarity in chemotaxis systems
We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.
Non-topological condensates in self-dual Chern-Simons gauge theory
This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.
Non-local Gel'fand problem in higher dimensions
The non-local Gel’fand problem, with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.
A blowup analysis of the mean field equation for arbitrarily signed vortices
We study the noncompact solution sequences to the mean field equation for arbitrarily signed vortices and observe the quantization of the mass of concentration, using the rescaling argument.
Duality and best constant for a Trudinger–Moser inequality involving probability measures
Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory
Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in and , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive convergence without any convergence rate....
Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory
Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in and , respectively, of the scheme are established. Under certain hypotheses on the data,...
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