Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems
Author
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-09-06
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Let X be a real locally uniformly convex reflexive separable Banach space with locally uniformly convex dual space X∗.
Let T:X⊇D(T)→2X∗ be maximal monotone and S:X⊇D(S)→X∗ quasibounded generalized pseudomonotone such that there exists a real reflexive separable Banach space W⊂D(S), dense and continuously embedded in X.
Assume, further, that there exists d≥0 such that 〈v∗+Sx,x〉≥-dx2 for all x∈D(T)∩D(S) and v∗∈Tx.
New surjectivity results are given for noncoercive, not everywhere defined, and possibly unbounded operators of the type T+S.
A partial positive answer for Nirenberg's problem on surjectivity of expansive mapping is provided.
Leray-Schauder degree is applied employing the method of elliptic superregularization.
A new characterization of linear maximal monotone operator L:X⊇D(L)→X∗ is given as a result of surjectivity of L+S, where S is of type (M) with respect to L.
These results improve the corresponding theory for noncoercive and not everywhere defined operators of pseudomonotone type.
In the last section, an example is provided addressing existence of weak solution in X=Lp(0,T;W01,p(Ω)) of a nonlinear parabolic problem of the type ut-∑i=1n(∂/∂xi)ai(x,t,u,∇u)=f(x,t), (x,t)∈Q; u(x,t)=0, (x,t)∈∂Ω×(0,T); u(x,0)=0, x∈Ω, where p>1, Ω is a nonempty, bounded, and open subset of RN, ai:Ω×(0,T)×R×RN→R (i=1,2,…,n) satisfies certain growth conditions, and f∈Lp′(Q), Q=Ω×(0,T), and p′ is the conjugate exponent of p.
American Psychological Association (APA)
Asfaw, Teffera M.. 2015. Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems. Abstract and Applied Analysis،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1052022
Modern Language Association (MLA)
Asfaw, Teffera M.. Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems. Abstract and Applied Analysis No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1052022
American Medical Association (AMA)
Asfaw, Teffera M.. Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems. Abstract and Applied Analysis. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1052022
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052022