Blow-up of solutions of strongly nonlinear equations of pseudoparabolic type

On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems

“…In the first case, we consider that 1 = l/4 ve 2 = l − 1 = 3l/4, and so l∕4 < −1 0 ln N l and 3l∕4 > l − −1 0 ln , h (1) = h (2)…”

“…It remains to estimate R for [ 1 , 2 ]. In this case since h (2) i = 2(l − 2 1 )N −1 l ≤ CN −1 l , we are able to write −1 h (2) i ∫…”

“…Equations of Sobolev type arise in many areas of mathematical physics and fluids mechanics. They are used to study consolidations of transmission lines ion-acoustic waves, plasmas waves in plasma for fluid flow in fissured rock, consolidation of clay, shear in second-order fluids, thermodynamics and propagation of long waves of small amplitude and other physical models ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein).…”

A sufficient condition for blowup of solutions to a class of pseudo‐parabolic equations with a nonlocal term

“…It often arises in the analysis of nonstationary processes in semiconductors in the presence of sources, where u t u t stands for the free electron density rate, u stands for the linear dissipation of free charge current, and juj p 1 u describes a source of free electron current [8]. In mathematics, since the work of Ting and Showalter [7,9], the pseudo-parabolic equations with b D c D 0 have attracted great attention; see [10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein. However, for the nonlocal case that c ¤ 0, the conclusions about the IBVP (1.1) are not many.…”

Second critical exponent and life span for pseudo-parabolic equation

“…In resent years considerable attentions have been paid to the study of pseudo-parabolic equations. Refer to [10,15,16,19,22,23] and references therein, where existence and uniqueness of solutions, regularity of solutions, optimal control problems, periodic problems, etc. were considered for various pseudo-parabolic equations.…”