Harkat, SoumiaGuesmia, Senoussi2020-09-222020-09-222019http://hdl.handle.net/123456789/9196Applying 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.enMonotone operatorHeat equationVariational inequalitieParabolic problemOther