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

Sagadeeva, M. A.; Rashid, A. S.

J. Comput. Eng. Math. 2, No. 2, 71-81 (2015).

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

Keywords:

degenerate strongly continuous semigroups; quasi-Banach spaces; Hille-Yosida-Feller-Miadera-Phillips theorem; modified Chen-Gurtin equation; quasi-Sobolev spaces