Degenerate Differential Equations in Banach Spaces
This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.
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Algebra analytic semigroup apply Theorem argument assumptions Banach space boundary conditions bounded inverse bounded linear operator bounded operator Cauchy problem Chapter closed linear operator coefficients continuous function converges deduce degenerate equations denotes densely defined differentiable semigroup differential operator Dirichlet boundary conditions domain equivalent estimate exists exponent Favini following result given function Hence Hilbert space holds Hq(Q implies initial condition initial value inner product interpolation couple interpolation spaces J. L. Lions Lemma Let us assume m. l. operator maximal regularity Moreover multiplication operator multivalued equation multivalued linear operator norm observe obtained partial differential equations possesses a unique proof of Theorem properties Proposition prove resolvent set resp satisfies Section selfadjoint single valued Sobolev subspace Theorem 5.1 Theory Tricomi equation un(t unique solution unique strict solution unknown function verified yields
Page 304 - Krein, Theory of self-adjoint extensions of semi-bounded Hermitian operators and its applications, I, Mat. Sb.
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