We use the steepest descent method in an Orlicz–Wasserstein space to study the existence of solutions for a very broad class of kinetic equations, which include the Boltzmann equation, the Vlasov–Poisson equation, the porous medium equation, and the parabolic p-Laplacian equation, among others. We combine a splitting technique along with an iterative variational scheme to build a discrete solution which converges to a weak solution of our problem.

中文翻译：

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Wasserstein空间中最陡下降的一类退化动力学方程的解

我们在Orlicz-Wasserstein空间中使用最速下降方法来研究一类非常广泛的动力学方程的解，其中包括Boltzmann方程，Vlasov-Poisson方程，多孔介质方程和抛物线p -Laplacian等式。我们将拆分技术与迭代变分方案相结合，以构建离散解决方案，该解决方案收敛到我们问题的弱解决方案。