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Linear and semilinear higher order parabolic equations in R-N

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Rodríguez Bernal, Aníbal and Cholewa, Jan W. (2010) Linear and semilinear higher order parabolic equations in R-N. Nonlinear Analysis: Theory, Methods & Applications, 75 (1). pp. 194-210. ISSN 0362-546X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X1100575X


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Abstract

In this paper we consider some fourth order linear and semilinear equations in R-N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1 < p < infinity prove that for a suitable family of Bessel potential spaces, H-p(alpha) (R-N), the linear equation defines a strongly continuous analytic semigroup.
Using this result, we prove that the nonlinear problems we consider can be solved for initial data in L-p(RN) and in H-p(2) (R-N). We also find the corresponding critical exponents, that is, the largest growth allowed for the nonlinear terms for these classes of initial data.


Item Type:Article
Uncontrolled Keywords:Interpolation spaces; Fractional powers of operators; Analytic semigroups; Initial value problems for higher order parabolic equations; Semilinear parabolic equations; Critical exponents; Critical Nonlinearities
Subjects:Sciences > Mathematics > Functions
ID Code:17660
Deposited On:15 Jan 2013 09:33
Last Modified:12 Dec 2018 15:07

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