Small perturbation of a semilinear pseudo-parabolic equation

This paper is concerned with large time behavior of solutions for the Cauchy problem of a semilinear pseudo-parabolic equation with small perturbation. It is revealed that small perturbation may develop large variation of solutions with the evolution of time, which is similar to that for the standard heat equation with nonlinear sources.

[1]  Qi S. Zhang.  A New Critical Phenomenon for Semilinear Parabolic Problems , 1998 .

[2]  M. Gurtin,et al.  On a theory of heat conduction involving two temperatures , 1968 .

[3]  Sining Zheng,et al.  Second critical exponent and life span for pseudo-parabolic equation☆ , 2012 .

[4]  J. Bona,et al.  Model equations for long waves in nonlinear dispersive systems , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  Iuliu Sorin Pop,et al.  A New Class of Entropy Solutions of the Buckley-Leverett Equation , 2007, SIAM J. Math. Anal..

[6]  Qi S. Zhang.  Blow Up and Global Existence of Solutions to an Inhomogeneous Parabolic System , 1998 .

[7]  Tsuan Wu Ting,et al.  Certain non-steady flows of second-order fluids , 1963 .

[8]  Jingxue Yin,et al.  Cauchy problems of semilinear pseudo-parabolic equations ✩ , 2009 .

[9]  Runzhang Xu,et al.  Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations , 2013 .

[10]  Ole Morten Aamo,et al.  Boundary control for a class of pseudo-parabolic differential equations , 2013, Syst. Control. Lett..

[11]  Ralph E. Showalter,et al.  Pseudoparabolic Partial Differential Equations , 1970 .

[12]  Xian-zhong Zeng.  Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations , 2007 .

[13]  J. Serrin,et al.  Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities , 2002 .

[14]  E. I. Kaikina,et al.  The Cauchy problem for an equation of Sobolev type with power non-linearity , 2005 .

[15]  Qi S. Zhang,et al.  Critical Exponents of Fujita Type for Inhomogeneous Parabolic Equations and Systems , 2000 .

[16]  The critical exponents for the quasi-linear parabolic equations with inhomogeneous terms , 2007 .

[17]  Andro Mikelić,et al.  A global existence result for the equations describing unsaturated flow in porous med , 2010 .

[18]  John R. King,et al.  Small- and Waiting-Time Behavior of a Darcy Flow Model with a Dynamic Pressure Saturation Relation , 2006, SIAM J. Appl. Math..

[19]  Andrea Terracina.  Qualitative Behavior of the Two-Phase Entropy Solution of a Forward-Backward Parabolic Problem , 2011, SIAM J. Math. Anal..