198 research outputs found
New-Type Solutions of the Modified Fischer-Kolmogorov Equation
We prove the existence of new-type solutions of the modified
Fischer-Kolmogorov equation with slow/fast diffusion and with possibly nonsmooth double-well potential. We show that a certain relation
between the rate of the diffusion and the smoothness of the potential may originate new type solutions which do not occur in the classical Fischer-Kolmogorov equation. The main focus of this paper is to show the sensitivity of the mathematical modelling with respect to the chosen form of the diffusion term and the shape of the double-well potential
A population biological model with a singular nonlinearity
summary:We consider the existence of positive solutions of the singular nonlinear semipositone problem of the form where is a bounded smooth domain of with , , , , and , , and are positive parameters. Here is a continuous function. This model arises in the studies of population biology of one species with representing the concentration of the species. We discuss the existence of a positive solution when satisfies certain additional conditions. We use the method of sub-supersolutions to establish our results
Periodic solutions for some phi-Laplacian and reflection equations
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular initial and boundary value problems with reflection, which allows us to prove existence of solutions of the latter using the existence of the formerThe work was partially supported by FEDER and Ministerio de Economía y Competitividad, Spain, project MTM2013-43014-P. The second author was supported by FPU scholarship, Ministerio de Educación, Cultura y Deporte, Spain and Xunta de Galicia (Spain), project EM2014/032S
Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions
We introduce an iterative method for computing the first eigenpair
for the -Laplacian operator with homogeneous Dirichlet
data as the limit of as , where
is the positive solution of the sublinear Lane-Emden equation
with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
to is in the -norm and the rate of convergence of
to is at least . Numerical evidence is
presented.Comment: Section 5 was rewritten. Jed Brown was added as autho
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