Blowup Of Solutions Of Two Classes Of Nonlinear Evolution Equations

This dissertation is devoted to the blow up estimates of the positive solutions totwo classes of nonlinear evolution equations.The dissertation includes three parts:In chapter 1,the basic application background,advanced studies,prelimininariesand the main ideas of this thesis are introduced.In chapter 2,I consider the following semilinear parabolic systemWhere m, p and q are nonnegative constants. B_R is the ball in R^N centered at theorigin with radius R,ηis the unit outward normal on (?)B_R. u₀(x), v₀(x) are assumedto be normegative and radially symmetric bounded continuous functions,v_r=(?)v/(?)r≥0(wherer=|x|) and satisfy the compatibility conditions.Through the Scaling method, the properties of Green function and somecomplex calculations, the blow-up estimates of the positive solutions are thenobtained. Also I give the affection of the blowup estimates from the reaction termsand the boundary absorption terms.Based on chapter 2, the equation v_t=â–³v is changed into v_t=â–³v+uⁿ in thechapter 3. By the similar way, I get the blow-up estimates of the positive solutionstoo, but the analysis is more complex than the chapter 2. Following, through themethod of undetermined coefficient, the method of super-sub solution andcomparison principle, the blow-up set of the solutions can be obtained in thedissertation.