An efficient generalization of the Rush--Larsen method for solving electro-physiology membrane equations.
An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems
This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and make it possible...
An eigenvalue problem for elliptic systems.
An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains
An eigenvalue problem related to Hardy’s inequality
An eigenvalue problem with mixed boundary conditions and trace theorems.
An elastic Green matrix for a semistrip.
An elastic membrane with an attached non-linear thermoelastic rod
We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence...
An electromagnetic free-boundary problem
An electrostatic inequality with applications to the constitution of matter
An Elementary Approach to Local Solvability for Constant Coefficient Partial Differential Equations.
An elementary approach to nonexistence of solutions of linear parabolic equations
This note presents an elementary approach to the nonexistence of solutions of linear parabolic initial-boundary value problems considered in the Feller test.
An Elementary Partial Regularity Proof for Vector-Valued Obstacle Problems.
An elementary proof for one-dimensionality of travelling waves in cylinders.
An Elementary Proof of Harnack's Inequality for Schrödinger Operators and Related Topics.
An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions.
An elementary theory of hyperfunctions and microfunctions
An Elliptic Boundary Value Problem Depending Nonlinearly Upon the Eigenvalue parameter.
An Elliptic Boundary Value problem occurring in Magnetohydrodynamcis.
An elliptic equation with no monotonicity condition on the nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...