By Fernando Casas, Vicente Martínez (eds.)
The e-book features a choice of contributions given on the 23th Congress on Differential Equations and functions (CEDYA) / thirteenth Congress of utilized arithmetic (CMA) that came about at Castellon, Spain, in 2013. CEDYA is popular because the congress of the Spanish Society of utilized arithmetic (SEMA) and constitutes the most discussion board and assembly element for utilized mathematicians in Spain. The papers incorporated during this e-book were chosen after an intensive refereeing approach and supply an outstanding precis of the hot task built via various teams operating more often than not in Spain on functions of arithmetic to a number of fields of technological know-how and expertise. the aim is to supply an invaluable reference of educational and business researchers operating within the quarter of numerical research and its applications.
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Additional info for Advances in Differential Equations and Applications
Pisa Cl. Sci. 22, 571–597 (1968) 17. : The general theory of the homogenization: a personalized introduction. Springer, Heidelberg/New York (2009) Weak Solutions to a Nonuniformly Elliptic PDE System in the Harmonic Regime María Teresa González Montesinos and Francisco Ortegón Gallego Abstract We study the existence of weak solutions to a nonlinear strongly coupled parabolic–elliptic PDEs arising in the heating induction-conduction process of steel hardening. In this setting, our major concern is to consider the case when the electric conductivity is nonuniformly elliptic which, together with a right hand side in L1 in the energy balance equation, yields to a difficult theoretical situation.
Pac. J. Math. 19(2), 285–346 (1966) 7. : Smoothing and perturbation for some fourth order linear parabolic equations in Rn . J. Math. Anal. Appl. 412(2), 1105–1134 (2014) 8. : Perturbation of analytic semigroups in scales of Banach spaces and applications to parabolic equations with low regularity data. SEMA J. 53, 3–54 (2011) 9. : Interpolation Theory, Function Spaces, Differential Operators. x/; x 2 ˝; ˝. ˝/ and the function f defined as f W ˝ R ! x; s/. We assume f globally Lipschitz or f locally Lipschitz in the variable s 2 R, uniformly with respect to x 2 ˝, and f satisfies that there exist C 2 R and D 0 such that f .
Ortegón Gallego Lemma 2 For every k lem (13)–(20). 'k ; Ak / for a given Âk . From that point on, the proof of Lemma 2 is a straightforward application of J. L. Lions’ theorem together with Schauder’s fixed point theorem. Âk /jr'k j 2 ˝T Z T kAk k2X Ä 0 C2 ˛! X/: On the other hand, since X ,! D/ Ä C kvkX , for all v 2 X. ˝//, for all 1 Ä p < 5=4; (25) Remark 3 In  it was shown that (25) holds true when dealing with homogeneous Dirichlet boundary conditions. In the case of homogeneous Neumann boundary conditions, this result was shown by Clain in .
Advances in Differential Equations and Applications by Fernando Casas, Vicente Martínez (eds.)