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Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case. (English) Zbl 1359.47041

Summary: 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.

MSC:

47D06 One-parameter semigroups and linear evolution equations
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46B45 Banach sequence spaces
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