### EXISTENCE OF SOLUTIONS IN QUASI-BANACH SPACES FOR EVOLUTIONARY SOBOLEV TYPE EQUATIONS IN RELATIVELY RADIAL CASE

#### Abstract

Sobolev-type equations (equations not solved for the highest derivative) probably first appeared in the late nineteenth century. The growing recent interest in Sobolev-type equations motivates us to consider them in quasi-Banach spaces. Specifically, this study aims at understanding non-classical models of mathematical physics in quasi-Banach spaces.

This paper carries over the theory of degenerate strongly continuous semigroups obtained earlier in Banach spaces to quasi-Banach spaces. We prove an analogue of the direct Hille-Yosida-Feller-Miyadera-Phillips theorem. As an application of abstract results, we consider the Showalter-Sidorov problem for modified linear Chen-Gurtin equations in quasi-Sobolev spaces.

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