In this paper, a priori estimate for a linear third pseudoparabolic operator with bound is established, and applying the above result, the existence and uniqueness theorem of solutions for a class of nonlinear pseudoparabolic equations is obtained with the help of the homeomorphism method and the initial value method. Furthermore, an existence and uniqueness theorem of the semilinear equation is obtained as a corollary.

中文翻译：

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一类三阶伪抛物方程的初边值问题

本文建立了带边界的线性第三拟抛物算子的先验估计，并应用上述结果，借助同胚方法和初值，得到了一类非线性拟抛物方程解的存在性和唯一性定理。值法。此外，推论得到了半线性方程的存在性和唯一性定理。