»ã±¨±êÌâ (Title)£ºA new augmented singular transform and its partial Newton-correction method for finding more solutions to nonlinear elliptic PDEs/systems (Ôö¹ãÆæ¹Ö±ä»»ÒÔ¼°Çó½â·ÇÏßÐÔÍÖԲƫ΢·Ö·½³ÌµÄÆ«Å£¶Ù-У¶Ô·¨)

»ã±¨ÈË (Speaker)£ºÀîÕÑÏé ½ÌÊÚ£¨ÉϺ£Ê¦·¶´óѧ£©

»ã±¨¹¦·ò (Time)£º2022Äê9ÔÂ3ÈÕ(ÖÜÁù) 15:00-16:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé £¨»áÒé ID£º464 499 443£©

Ô¼ÇëÈË(Inviter)£º²ÌÃô

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»ã±¨ÌáÒª£ºIn this talk, in order to find more solutions to nonlinear elliptic systems, a new augmented singular transform (AST) is developed to form a barrier surrounding previously found solutions so that an algorithm search from outside cannot pass the barrier and penetrate into the inside to reach a previously found solution. Thus, a solution found by the algorithm must be new. Mathematical justifications of AST formulation are established. A partial Newton-correction method is designed accordingly to solve the augmented problem and to satisfy a constraint in AST. The new method is applied to numerically investigate multiple solutions to nonlinear elliptic systems by Legendre-Gauss-lobatto pseudospectral method.