Browsing by Author "Guesmia, Senoussi"

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    Asymptotic analysis of some singular perturbation problems
    (université Oum-El-Bouaghi, 2018) Azouz, Salima; Guesmia, Senoussi
    In the present work we focus on the analysis of the asymptotic behaviour of the solutions to anisotropic singular perturbation boundary value problems. A complete description of the asymptotic behaviour on the whole domain of definition is established. Two types of functions are constructed. The first type acts far away from the boundary layers to give the best possible approximation. The second one deals with the behaviour near the boundary layers to recover the complete approximation with a sharper rate of convergence. In fact, we go beyond the limit behaviour by considering the regular and the composite asymptotic expansions of arbitrary order. This allows to get an asymptotic approximation of a polynomial rate of convergence in arbitrary order or even an exponential one.
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    Asymptotic behaviour of solutions to some nonlinear problems
    (University Of Oum El Bouaghi, 2019) Harkat, Soumia; Guesmia, Senoussi
    Applying an asymptotic method, the existence of the minimal solution to some variational elliptic inequalities defined on bounded or unbounded domains is established. As well, the large time behavior of the solution to some evolution problems on time-dependent domains becoming unbounded in many directions when t tends to infinity is dealt with. The convergence and its rate are also investigated with respect to the growth rate of the domain when t ??. The steady state solution and its existence for nonlinear parabolic problems is already investigated when we deal with the variational elliptic inequalities. Since the convergence cannot be expected on the whole domain correctors are built to describe the asymptotic behaviour, of the solution of Heat equation, in the distant regions. ÈÊØÈíÞ ØÑíÞÉ ãÞÇÑÈÉ ¡ íÊã ÊÍÏíÏ æÌæÏ ÇáÍá ÇáÃÏäì áÈÚÖ ÃæÌå ÚÏã ÇáãÓÇæÇÉ ÇáÅåáíáÌíÉ ÇáãÊÛíÑÉ ÇáãÍÏÏÉ Ýí ÇáãÌÇáÇÊ ÇáãÍÕæÑÉ Ãæ ÛíÑ ÇáãÍÏæÏÉ. ßÐáß ¡ ÝÅä Óáæß æÞÊ ßÈíÑ ãä Íá áÈÚÖ ãÔÇßá ÇáÊØæÑ Úáì ÇáãÌÇáÇÊ ÇáãÚÊãÏÉ Úáì ÇáæÞÊ ÊÕÈÍ ÛíÑ ãÍÏæÏÉ Ýí ÇáÚÏíÏ ãä ÇáÇÊÌÇåÇÊ ÚäÏãÇ íÊã ÇáÊÚÇãá ãÚ t ÇááÇäåÇíÉ. íÊã ÇáÊÍÞíÞ Ýí ÇáÊÞÇÑÈ æãÚÏáå ÃíÖðÇ ÝíãÇ íÊÚáÞ ÈãÚÏá äãæ ÇáãÌÇá ÚäÏ t ¿¿. Åä Íá ÇáÍÇáÉ ÇáãÓÊÞÑÉ ææÌæÏå áãÔÇßá ãßÇÝÆíÉ ÛíÑ ÎØíÉ íÊã ÇáÊÍÞíÞ Ýíå ÈÇáÝÚá ÚäÏãÇ äÊÚÇãá ãÚ ÃæÌå ÚÏã ÇáãÓÇæÇÉ ÇáÅåáíáÌíÉ ÇáãÊÛíÑÉ. ãäÐ ÇáÊÞÇÑÈ áÇ íãßä ÊæÞÚå Úáì ßÇãá ÇáãÌÇá ãÕÍÍÇÊ ÈäíÊ á æÕÝ ÇáÓáæß ÛíÑ ÇáãÞÇÑÈ ¡ Ýí Íá ãÚÇÏáÉ ÇáÍÑÇÑÉ ¡ Ýí ÇáãäÇØÞ ÇáÈÚíÏÉ. Applying an asymptotic method, the existence of the minimal solution to some variational elliptic inequalities defined on bounded or unbounded domains is established. As well, the large time behavior of the solution to some evolution problems on time-dependent domains becoming unbounded in many directions when t tends to infinity is dealt with. The convergence and its rate are also investigated with respect to the growth rate of the domain when t ??. The steady state solution and its existence for nonlinear parabolic problems is already investigated when we deal with the variational elliptic inequalities. Since the convergence cannot be expected on the whole domain correctors are built to describe the asymptotic behavior, of the solution of Heat equation, in the distant regions.