Pablo Álvarez Caudevilla
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Titular de Universidad
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List of Publications
- Existence and multiplicity of stationary solutions for a Cahn--Hilliard-type equation in RN, Discrete Contin. Dyn. Syst. AIMS Proceedings, in press/accepted.
- Countable families of solutions of a limit stationary semilinear fourth-order Cahn--Hilliard-type equation I. Mountain pass and Lusternik--Schnirel'man patterns in R^N, (with Jonathan D. Evans and Victor Galaktionov), submitted.
- Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations, (with Eduardo Colorado and Victor Galaktionov), Nonlinear Analysis: Real World Applications, 23, (2015), 78-93.
- On a Branching Analysis of a countable family of global similarity solutions of a fourth-order thin film equation, (with Victor A.Galaktionov), Electronic Journal of Differential Equations, Vol. 2015 (2015), no. 90, 1-29.
- "Blow-up" and global behaviour of the solutions of the bi-Laplace equation in domains with a multiple crack section, (with Victor A. Galaktionov), Communications in Pure and Applied Analysis, in press.
- Towards optimal regularity for the fourth-order thin film equation in R^N: Graveleau-type focusing self-similarity, (with Jonathan D. Evans and Victor A. Galaktionov), Journal of Mathematical Analysis and Applications, 431 (2015), 1099-1123.
- The p-Laplace equation in domains with a multiple crack section via pencil operators, (with Victor A. Galaktionov), Advances Nonlinear Studies, 15, no. 1 (2015), 91-116.
- The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions, (with Jonathan D. Evans and Victor A. Galaktionov), Discrete Contin. Dyn. Syst., 35, no. 3 (2015), 807-827.
- Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches, (with Victor A.Galaktionov), Nonlinear Analysis, 121 (2015), 19-35.
- Qualitative analysis of a cooperative reaction-diffusion system in spatiotemporally degenerate environment, (with Yihong Du and Rui Peng), SIAM Journal of Mathematical Analysis, vol. 46, no. 1 (2014), 499-531.
- The Cauchy problem for tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions, (with Jonathan D. Evans and Victor A. Galaktionov) Mediterranean Journal of Mathematics, No. 4, Vol. 10(2013), 1759-1790.
- Steady states, global existence and blow--up for fourth--order semilinear parabolic equations of Cahn--Hilliard type, (with Victor A.Galaktionov) Advances Nonlinear Studies, 12, (2012), 315-361.
- Variational approach for a class of cooperative systems, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 5620-5638.
- Local bifurcation analysis of global and “blow-up” patterns for a fourth-order thin film equation, Nonlinear Differential equations and Applications (NoDEA), Vol. 18, (2011), 483--537, (with Victor A.Galaktionov).
- Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence, Advances in Differential Equations, Vol. 15, 7-8 (2010), 649-688, (with Antoine Lemenant).
- The dynamics of a class of sublinear cooperative systems, Discrete Contin. Dyn. Syst. 26, no. 2, (2010), 397–415, (with Julián López-Gómez).
- Characterizing the existence of coexistence states for a class of cooperative systems, Discrete Contin. Dyn. Syst., Supplement (2009), 24–33, with Julián López-Gómez).
- Asymptotic behaviour of principal eigenvalues for a class of cooperative systems [Corrigendum J. Differential Equations 245, (2008), no. 2, 566–567], Journal of Differential Equations. 244 (2008), 1093–1113, (with Julián López-Gómez).
- Semiclassical Analysis for highly degenerate potentials. Proceedings of American Mathematical Society, 136 (2008), 665–675, (with Julián López-Gómez).
- Metasolutions in cooperative systems, Nonlinear Analysis: Real World Applications. 9 (2008), 1119–1157, (with Julián López-Gómez).
Teaching
Academic Year 2018-2019.
- Undergraduate Teaching.
- Advanced Mathematics (Differential Equations). Second year Bachelor' Degree in Aerospace Engineering (in English).
- Advanced Mathematics (Complex Variable and ODEs). Second year Bachelor' Degree in Audiovisual Systems Engineering.
- Calculus III. Third year Bachelor' Degree in Industrial Technologies Engineering (in English).
- Advanced Mathematics (Linear Algebra). Second year Bachelor' Degree Statistics and Business.
- Postgraduate Teaching. Partial Differential Equations. Masters in Mathematical Engineering.
Academic Year 2010-2018.
- Undergraduate Teaching.
- Calculus I. First year Bachelor' Degree in Mechanical Engineering (in English).
- Calculus II. First year Bachelor' Degrees in Biomedical Engineering (in English) Industrial Technologies and Telematic Engineering.
- Calculus III. Third year Bachelor' Degree in Industrial Technologies Engineering (in English).
- Differential Equations. Second year Bachelor' Degree in Biomedical Engineering (in English).
- Advanced Mathematics (Differential Equations). Second year Bachelor' Degree in Aerospace Engineering (in English).
- Postgraduate Teaching. Partial Differential Equations and Advanced Numerical Methods. Masters in Mathematical Engineering.