Geodesic
Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case
Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 71-81

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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. 
@article{JCEM_2015_2_2_a6,
     author = {M. A. Sagadeeva and A. S. Rashid},
     title = {Existence of solutions in {quasi-Banach} spaces for evolutionary {Sobolev} type equations in relatively radial case},
     journal = {Journal of computational and engineering mathematics},
     pages = {71--81},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a6/}
}
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M. A. Sagadeeva; A. S. Rashid. Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case. Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 71-81. http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a6/