粒子表面の微小変形を考慮した極性流体の輸送方程式の混合問題に関する研究　第３報　非完全反射壁の場合の弱い解の一意存在定理，正値性，比較定理

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  • On Mixed Problems of Transport Equations of Polar Fluids with Infinitesimal Particle Surface Deformation. 3rd Report. Unique Existence Theorem for a Weak Solution under Imperfect Reflective Barrier Boundary Conditions, Positive-Valued Property and Comparison Theorem.

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In a previous report, we proposed a statistical theory for powder surface modification technology by means of a mechanical method using the transport equations of polar fluids with infinitesimal particle surface deformation. In this paper, we demonstrate the unique existence theorem for a weak solution on a mixed problem under imperfect reflective barrier boundary conditions (∥MB∥<1) by a priori evalution and the successive approximation method. We consider the relationship between weak solutions and other improper solutions, such as strong solutions and almost-everywhere solutions. The positive-valued property and the comparison theorem for weak solutions are proven by positive operators to assign the physical meaning to improper solutions.

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