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

M. A. Sagadeeva, A. S. Rashid

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.


Keywords


degenerate strong continuous semigroups; quasi-Banach spaces; Hille-Iosida-Feller-Miadera-Phillips theorem; modified Chen-Gurtin equation; quasi-Sobolev spaces.

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References


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