SIGN-CHANGING SOLUTIONS OF A QUASILINEAR HEAT EQUATION WITH A SOURCE TERM
Abbreviated Journal Title
Discrete Contin. Dyn. Syst.-Ser. B
Quasilinear heat equation; self-similar; compact support; sign-changing; asymptotic estimates; ORDINARY DIFFERENTIAL-EQUATION; RAPIDLY DECAYING SOLUTIONS; HARAUX-WEISSLER EQUATION; NONUNIQUENESS; EXISTENCE; Mathematics, Applied
The Cauchy problem of a heat equation with a source term psi = Delta (vertical bar psi vertical bar(m-1)psi) + vertical bar psi vertical bar(gamma-1)psi in (0, infinity) x R-n is considered, where gamma > m > 1. We are interested in global solutions with Holder continuity which satisfy the equation in the distribution sense, and with a fixed number of sign changes at any given time t > 0. Through detailed analysis of the self-similarity problem, we prove the existence of two type of such solutions, one with compact support and the other decays to zero as vertical bar x vertical bar -> infinity with an algebraic rate determined uniquely by n, m and gamma. Our results extend previous study on positive self-similar solutions. Moreover, they demonstrate vital difference from the well-studied semi-linear case of m = 1.
Discrete and Continuous Dynamical Systems-Series B
"SIGN-CHANGING SOLUTIONS OF A QUASILINEAR HEAT EQUATION WITH A SOURCE TERM" (2013). Faculty Bibliography 2010s. 4321.