关于锂离子电池内部温度模型的存在性定理
An Existence Theorem for a Model of Temperature Within a Lithium-Ion Battery
AI总结：
本文研究锂离子电池温度模型，克服了由 Butler-Volmer 方程及电势梯度平方项带来的非线性困难，证明了连续温度的局部存在性。
摘要：
本文研究锂离子电池内部的温度模型。该模型由关于温度的抛物型偏微分方程与分别描述固相和电解质相中电势的两个椭圆型偏微分方程耦合而成。主要困难源于由 Butler-Volmer 方程给出的耦合项，该方程对电势及温度的倒数均呈指数非线性。温度方程的另一难点在于右侧出现的电势梯度平方项。由于非线性，目前尚无温度的有效估计。尽管如此，研究仍证明了锂离子电池连续温度的局部存在性。
英文摘要：
In this article we investigate a model for the temperature within a Lithium-Ion battery. The model takes the form of a parabolic PDE for the temperature coupled with two elliptic PDE's for the electric potential within the solid and electrolyte phases. The primary difficulty comes from the coupling term, which is given by the Butler-Volmer equation. It features an exponential nonlinearity of both the electric potentials and the reciprocal of the temperature. Another difficulty arising in the temperature equation are the gradients of the electric potentials squared showing up on the right-hand side. Due to the nonlinearity, meaningful estimates for the temperature are currently not known. In spite of this, our investigation reveals the local existence of continuous temperature for the Lithium-Ion Battery.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
