Qualitative methods: for nonlinear partial derivative equations
Keywords:
equations, physics, engineering, derivativesSynopsis
The theory of equations in partial derivatives plays a very important role in contemporary Physics-Mathematics theory, since such equations naturally have application in various areas of science such as physics, chemistry, engineering, biology and other fields. The case of periodic baseline data is relatively new in the literature. The problem that we will deal with in your linear and non-linear case is of the wave type, that is, of the hyperbolic type. Also in the last chapter we worked on a parabolic equation and introduced techniques for this type of problem, which in our case will be a Burgers equation. These techniques are based on Banach's fixed point theorem, and similar to what is done in EDO, these techniques are strong enough to be called qualitative techniques in EDP, which motivates the title of our book.
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References
N. Hayashi; P. Naumkin; J.Rodriguez-Ceballos. Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation. Nonlinear Differ. Equ. Appl. 17. 355- 369. 2010.
F. Linares. Ecuaciones dispersivas no lineales. Caso periódico. Caracas: Escuela Venezolana de Matemáticas. 2007.
P. Naumkin; J. Rodríguez-Ceballos. Estimaciónes en los espacios de Sobolev de la solución del problema de Cauchy. Matemáticas: Enseñanza Universitaria. pp.31-40. 2009.
P. Naumkin; C. Rojas Milla. Soluciones asintóticas para un problema no lineal de onda. Tesis Doctoral. 2011.
A. Marín; C. Rojas; R. Ortiz. Solutions for the nonlinear damped wave equation. International Journal of Mathematical Analysis. 2015.
H. Brézis. Análisis funcional, teoría y aplicaciones. Masson, París, Ed. cast.: Alianza Editorial S.A. Madrid. 1984.
J. Sotomayor. Licoes de equacoes diferenciais ordinárias. Instituto de Matemáticas Pura e Aplicada. 1979.
V. P. Mijailov. Ecuaciones diferenciales en derivadas parciales. Editorial MIR Moscú. 1978.
Rafael Iório; Valería Iório. Equeacoes diferenciais parciais. Uma introducao. CNPq (Proyecto Euclides). 1998.
A. Pazy. Semigroups of linear operators and applications to partial diferential equations. Aplpplied mathematical sciences; v.44 Springer Verlag, New York, Inc. 1983.
N. Hayashy; E.I. Kaikina; P. Naumkin. Damped wave equation whit a critical nonlinearity. Trans.Am Math.soc. 358(3), 1165. 2006.
N. Hayashy; E.I. Kaikina; P. Naumkin. Damped wave equation in the subcritical cases.J. Differential Equation. 207(1), 161-194. 2004.
N. Hayashy; E.I. Kaikina; P. Naumkin; I.A. Shishmarev Damped wave equation in the subcritical cases.J. Differential Equation. 207(1), 161-194. 2009.
P. Naumkin; C. Rojas Asymptotics of solutions to the periodic Problem for a burguer type equation J. Evol. Equa. Springer Basel AG-DOY10.1007. 2010.
H. Amman Dinamic theory of quasilinear parabolic systms. Global existence. Math Z202 No.2, 219-250. 1989.
A. Constantin; J. Escher Global solutions for quasilinear parabolic problems Evol. Equ 2(2002) Nro. 1,97-11.Doering, CR., Gibbon.
E.I. Kaikina; P.I. Naumkin; I.A. Shishmarev Periodic problem for a model nonlinear evolution equation Adv.Differ.Equ. 7(5), 581-616(2002)
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Published
September 25, 2018
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Details about this monograph
ISBN-13 (15)
978-958-5525-40-5
Publication date (01)
2018
