11 citations · 20 across the 14 of their papers we have counts for
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Numerical verification method for positive solutions of elliptic problems
Kazuaki Tanaka
The purpose of this paper is to propose methods for verifying the positivity of a weak solution of an elliptic problem assuming -error estimation $ \left\|u-\hat{u}\…
A posteriori verification of the positivity of solutions to elliptic boundary value problems
Kazuaki Tanaka, Taisei Asai
The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither -regula…
Numerical verification for asymmetric solutions of the Hénon equation on bounded domains
Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi
The Hénon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore,…
A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations
Kazuaki Tanaka
This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogen…