Bubble-type solutions of nonlinear singular problems

Authors:
Irena Rachnková;Jan TomečEk
Affiliations:
Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic;Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

Citing 2
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Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics

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Analytical-numerical investigation of bubble-type solutions of nonlinear singular problems

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Analysis and numerical approximation of singular boundary value problems with the p-Laplacian in fluid mechanics

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Abstract

The paper describes the set of all solutions of the singular initial problems (p(t)u^')^'=p(t)f(u),u(0)=B,u^'(0)=0, on the half-line [0,~). Here B0 on (0,~), f(L)=0 for some L0 and xf(x)0. By means of this result, the existence of a strictly increasing solution of this problem satisfying u(~)=L is proved under some additional assumptions. In particular cases this homoclinic solution determines an increasing mass density in centrally symmetric gas bubbles which are surrounded by an external liquid with density L.