Russian
| English
"Куда идет мир? Каково будущее науки? Как "объять необъятное", получая образование - высшее, среднее, начальное? Как преодолеть "пропасть двух культур" - естественнонаучной и гуманитарной? Как создать и вырастить научную школу? Какова структура нашего познания? Как управлять риском? Можно ли с единой точки зрения взглянуть на проблемы математики и экономики, физики и психологии, компьютерных наук и географии, техники и философии?"

«REGIONAL, SINGLE POINT, AND GLOBAL BLOW-UP FOR THE FOURTH-ORDER POROUS MEDIUM TYPE EQUATION WITH SOURCE» 
V.A. Galaktionov

On classic second-order blow-up models and higher-order diffusion. Blowup phenomena as intermediate asymptotics and approximations of highly nonstationary processes are common and well known in various areas of mechanics and physics. Theorigin of intensive systematic studies of such nonlinear effects was gas dynamics (since the end of the 1930s and 1940s) supported later in the 1960s by plasma physics (wave collapse) and nonlinear optics (self-focusing phenomena). Nevertheless, it was reaction-diffusion theory that exerted the strongest influence on mathematical blow-up research since the 1970s. It is not an exaggeration to say that precisely reaction-diffusion theory proposed basic and canonical nowadays models, which eventually led to qualitative and rigorous description of principles of formation of blow-up and other singularities in nonlinear PDEs.

Read (PDF) >>