廣義BBM-Burgers方程解的長時間漸近性估計.pdf

1、浙江大學理學院碩士學位論文廣義BBMBurgers方程解的長時間漸近性估計姓名：蔡蘇蘭申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：薛儒英20090501AbstractInthispaperwediscusslocalexistenceandglobalexistenceofsolutionsandthelargetimeasymptoticbehaviorofthesolutionfortheCauchyproblemaboutthen

2、extBenjaminBonaMahony—Burgersequation(forbrevitywecallitBBMBurgersequation)：毗一u$科一“zz二二!薔蘭2i三z∈Rt0z∈酞ApplyingthetheoryoftheSobolevspaceandcontractionmappingprinciple，weprovedthereexistsauniqueglobalsolution心∈c([o，∞)；礦(R)

3、nLL口(R))nc((o，o。)；w三(R))totheCauchyproblemfortheBBMBurgersequationwhentheinitialdatau0∈p(酞)nL1m(R)(inwhich盯1a∈(0，1】，P盯)andthenormIluollL。II銣|lpsmallenoughMoreoverthesolutionu(x，t)hasthefollowinglargetimeasymptoticsu(z，亡)