Results 11 to 20 of about 53 (53)

Sign changing solutions of Poisson's equation

Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020
Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
wiley   +1 more source

On the relativistic heat equation in one space dimension

Proceedings of the London Mathematical Society, Volume 107, Issue 6, Page 1395-1423, December 2013., 2013
We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behaviour.
J. A. Carrillo, V. Caselles, S. Moll
wiley   +1 more source

Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 14, Page 721-739, 2004., 2004
We study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves.
S. Shao, C. L. Chang
wiley   +1 more source

On the solutions of nonlinear initial‐boundary value problems

Abstract and Applied Analysis, Volume 2004, Issue 5, Page 407-424, 2004., 2004
We deal with the general initial‐boundary value problem for a second‐order nonlinear nonstationary evolution equation. The associated operator equation is studied by the Fredholm and Nemitskii operatortheory. Under local Hölder conditions for the nonlinear member, we observe quantitative and qualitative properties of the set of solutions of the given ...
Vladimír Ďurikovič, Monika Ďurikovičová   +1 more
wiley   +1 more source

Asymptotic solutions of diffusion models for risk reserves

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 35, Page 2221-2239, 2003., 2003
We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the
S. Shao
wiley   +1 more source

On the weak solution of a three‐point boundary value problem for a class of parabolic equations with energy specification

Abstract and Applied Analysis, Volume 2003, Issue 10, Page 573-589, 2003., 2003
This paper deals with weak solution in weighted Sobolev spaces, of three‐point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation.
Abdelfatah Bouziani
wiley   +1 more source

Rothe method for a mixed problem with an integral condition for the two‐dimensional diffusion equation

Abstract and Applied Analysis, Volume 2003, Issue 16, Page 899-922, 2003., 2003
This paper deals with an initial boundary value problem with an integral condition for the two‐dimensional diffusion equation. Thanks to an appropriate transformation, the study of the given problem is reduced to that of a one‐dimensional problem. Existence, uniqueness, and continuous dependence upon data of a weak solution of this latter are proved by
Nabil Merazga, Abdelfatah Bouziani
wiley   +1 more source

Time‐dependent Stokes equations with measure data

Abstract and Applied Analysis, Volume 2003, Issue 17, Page 953-973, 2003., 2003
We establish the existence of a unique solution of an initial boundary value problem for the nonstationary Stokes equations in a bounded fixed cylindrical domain with measure data. Feedback laws yield the source and its intensity from the partial measurements of the solution in a subdomain.
Bui An Ton
wiley   +1 more source

On the existence of positive solutions for periodic parabolic sublinear problems

Abstract and Applied Analysis, Volume 2003, Issue 17, Page 975-984, 2003., 2003
We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problems Lu = g(x, t, u) in Ω × ℝ (where Ω ⊂ ℝN is a smooth bounded domain) for a wide class of Carathéodory functions g : Ω × ℝ × [0, ∞) → ℝ satisfying some integrability and positivity conditions.
T. Godoy, U. Kaufmann
wiley   +1 more source

Variational analysis for simulating free‐surface flows in a porous medium

Journal of Applied Mathematics, Volume 2003, Issue 8, Page 377-396, 2003., 2003
A variational formulation has been developed to solve a parabolic partial differential equation describing free‐surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two‐dimensional domain.
Shabbir Ahmed, Charles Collins
wiley   +1 more source