in what way could ozymandias be said to live on?

"Ozymandias," by Percy Bysshe Shelley, is a variation on a type of poem that proclaims its own monumental nature and importance. The most important poem of this genre, and one that had immense subsequent influence, was by Horace. In Ode 3.30, Horace claims that in his poetry, "I have created a monument more lasting than bronze."
This claim has been repeated by numerous poets, including Shakespeare in Sonnet 55: "Not marble, nor the gilded monuments / Of princes, shall outlive this powerful rhyme."
In "Ozymandias," Shelley participates in this tradition of showing how the monumental nature of art outlasts the wealthy and powerful people portrayed in artistic or literary creations. At first, a reader might think that Shelley addresses the theme ironically, as even the monumental sculpture is fallen and half-buried in the sand. However, since the poem itself immortalizes Ozymandias, in fact, the import of the poem is to suggest, as Shakespeare did, that the words of the poet are more durable than even monumental statuary. Thus Ozymandias himself lives on as the subject of Shelley's poem.