Existence of a unique solution to a quasilinear elliptic equation |
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Authors: | D Denny |
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Institution: | Department of Mathematics and Statistics, Texas A&M University - Corpus Christi, Corpus Christi, TX 78412, United States |
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Abstract: | The purpose of this paper is to prove the existence of a unique classical solution u(x) to the quasilinear elliptic equation −∇⋅(a(u)∇u)+v⋅∇u=f, where u(x0)=u0 at x0∈Ω and where n⋅∇u=g on the boundary ∂Ω. We prove that if the functions a, f, v, g satisfy certain conditions, then a unique classical solution u(x) exists. Applications include stationary heat/diffusion problems with convection and with a source/sink, where the value of the solution is known at a spatial location x0∈Ω, and where n⋅∇u is known on the boundary. |
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Keywords: | Existence Uniqueness Quasilinear Elliptic |
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