A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids

Nachman, A.; Callegari, Andrew J.

doi:10.1137/0138024

Cited by 329 publications

(109 citation statements)

References 9 publications

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“…In this paper we assume h(x) only integrable and use the Schauder fixed point theorem and elliptic estimates. Singular equations appear in the theory of heat conduction in electrically conducting materials, (Fulks and Maybee [6]), in binary communications by signals (Nowosad [1]) and in the theory of pseudoplastic fluids (Nachman and Callegari [7]). …”

Section: K(x Y)(u(x)) −γ Dymentioning

confidence: 99%

Singular nonlinear elliptic equations in Rⁿ

Alves

Gonçalves

Maia

1998

Abstract and Applied Analysis

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Abstract. This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the formwhere a, h are given, not necessarily continuous functions, and γ is a positive number. We explore both situations where a, h are radial functions, with a being eventually identically zero, and cases where no symmetry is required from either a or h. Schauder's fixed point theorem, combined with penalty arguments, is exploited.

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Section: K(x Y)(u(x)) −γ Dymentioning

confidence: 99%

Singular nonlinear elliptic equations in Rⁿ

Alves

Gonçalves

Maia

1998

Abstract and Applied Analysis

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“…In the case N = 1 , this problem arises in certain problems in fluid mechanics and pseudoplastic flow [6], [7]. The TV-dimensional problem (1) has been studied in [1] for general regions and, in [2], under the assumption that Si is the open unit ball in R^ and p(x) = q(\x\), where q is a continuous function which is defined continuous and nonnegative on [0, 1).…”

Section: Introductionmentioning

confidence: 99%

On a Singular Nonlinear Elliptic Boundary-Value Problem

Lazer¹,

McKenna²

1991

Proceedings of the American Mathematical Society

110

127

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“…A comparison with the existing mathematical literature on singular elliptic boundary value problems revealed a curious gap: namely, there is a considerable amount of knowledge on the singular semilinear elliptic boundary value problem (1.1) u{x)7Au + p(x) = 0, (1.2) «bn = 0, where £2 is a sufficiently regular bounded domain in RN, N > 1 , and p is a sufficiently regular function which is positive on Q. In the case N -1 , this problem arises in certain applications in fluid mechanics and pseudoplastic flow (see [5,6,7]). The /V-dimensional problem (1.1)-(1.2) has been studied in [2] for general regions.…”

Section: Introductionmentioning

confidence: 99%