-
TRNG I HC HNG VNGKHOA TON CNG NGH
BO CO TI NGHIN CU KHOA HC SINH VIN
-
BO CO TI NGHIN CU KHOA HC SINH VINTP HT TON CC CA PHNG TRNH PHN
NG KHUCH TN Nhm ngnh: TN1 Loi hnh nghin cu : C bn
Ch nhim ti: NG NGC TNCng tc vin: 1. L PHAN THY DNG 2. TRN TH THU
THYGing vin hng dn: Th.S NG TH PHNG THANH
-
1.TNG QUAN TNH HNH NGHIN CU THUC LNH VC TI
Nghin cu phng trnh phn ngkhuch tn cho ta bit mt s kt qu nh tnh t
ng, tnh trn ca nghim, s tn ti tp ht ton cc, tp ht li, nh gi s chiu
ca tp ht ...Trong Ton hc, cc kt qu t c khi nghin cu phng trnh phn
ng khuch tn ch yu tp trung trong cc trng hp khc nhau ca hm ngoi lc
v hm phi tuyn
-
2.TNH CP THIT CA TI
Trng hp hm ngoi lc tha mn iu kin tng trng v tiu hao kiu a thc
hoc kiu Sobolev c nghin cu trong nhiu ti liu tham kho. Cc kt qu t c
l tnh t ng, tnh trn ca nghim, s tn ti tp ht ton cc, tp ht li, nh gi
s chiu ca tp ht .... m rng nhng kt qu nghin cu trn, chng ti xt bi
ton phng trnh phn ng khuch tn vi hm phi tuyn tha mn iu kin tng trng
kiu mi (tng ng kiu m), rng hn so vi nhng kt qu c (kiu Sobolev v kiu
a thc).
-
3. MC TIU TI Mc tiu ca ti l da vo cc kt qu nghin cu v tp ht ton
cc ca phng trnh phn ng - khuch tn trong trng hp hm ngoi lc tha mn
iu kin tng trng kiu a thc chng minh s tn ti v duy nht nghim, s tn
ti tp ht ton cc ca phng trnh phn ng khuch tn trong trng hp hm ngoi
lc tha mn iu kin tng trng kiu m.
-
4.I TNG, PHM VI NGHIN CU- i tng nghin cu: Phng trnh phn ng -
khuch tn phi tuyn- Phm vi nghin cu: Phng trnh phn ng khuch tn trong
trng hp hm ngoi lc tha mn iu kin tng trng kiu a thc v kiu m
-
5. NI DUNG NGHIN CUNgoi phn mc lc, m u v ti liu tham kho, ti d
kin chia thnh 3 chng nh sau:
Chng I: Kin thc c s 1.1 Cc khng gian hm 1.2 Mt s bt ng thc v nh
l c bn 1.3 L thuyt tng quan v tp ht ton cc
-
5. NI DUNG NGHIN CUChng II: Tp ht ton cc ca phng trnh phn ng
khuch tn phi tuyn vi hm phi tuyn tha mn iu kin tng trng kiu a thc
2.1 t bi ton. 2.2 S tn ti v duy nht ca nghim yu 2.3 S tn ti tp ht
ton cc Chng III: Tp ht ton cc ca phng trnh phn ng khuch tn phi tuyn
vi hm phi tuyn tha mn iu kin tng trng kiu m 3.1 t bi ton. 3.2 S tn
ti v duy nht ca nghim yu 3.3 S tn ti tp ht ton cc
-
6. TI LIU THAM KHOCung Th Anh (2012), C s l thuyt h ng lc v hn
chiu, NXB i hc s phm H Ni.Nguyn Minh Chng (2000), Phng trnh o hm
ring tuyn tnh, NXB Gio dc.Nguyn Mnh Hng (2010), Phng trnh o hm ring
tuyn tnh, NXB i hc s phm H Ni.Trn c Vn (2008), L thuyt phng trnh vi
phn o hm ring, NXB i hc Quc gia H Ni..L.C. Evan (1998), Partial
Differential Equations, AMS.J. L. Lions, Quelques Mthodes de
Rsolution des Problmes aux Limites non Linaires, Dunod, Paris,
1969.R. Temam (1997), Infinite Dimensional Dynamical Systems in
Mechanics and Physics, 2nd edition, Springer-Verlag, New York.B.
Wang (1999), Attractors for reaction-diffusion equations in
unbounded domains, Physica D 179, 41-52.
-
Cm n thy c v cc bn !Nhm sinh vin thc hin ti :1. NG NGC TN2. L
PHAN THY DNG3. TRN TH THU THY n v: Lp K12 HSP Ton - Khoa Ton &
CN
* knh cho cc thy c gio v cc bn sv .tn e l ...thay mt nhm e xin k
thuyt trnh ti :...,**
