Self-similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation
نویسندگان
چکیده
منابع مشابه
On convergence towards a self-similar solution for a nonlinear wave equation - a case study
We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate nu...
متن کاملOn the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture
The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...
متن کاملNonlinear wave evolution equation for critical layers.
Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...
متن کاملSelf-similar solutions to a coagulation equation
The existence of self-similar solutions with a finite first moment is established for the Oort-Hulst-Safronov coagulation equation when the coagulation kernel is given by a(y, y∗) = yλ + yλ ∗ for some λ ∈ (0, 1). The corresponding self-similar profiles are compactly supported and have a discontinuity at the edge of their support. MSC 2000: 45K05, 45M05, 82C21
متن کاملOn the Asymptotic Growth of Solutions to a Nonlinear Equation
so our results will hold for solutions of (2). We shall be primarily interested in the nonlinear oscillator, i.e. a(t)>0, xg(x)>0 for x^O, but in Theorem III below, sign restrictions are removed. If we consider h(t) to be a sample function of a Brownian motion process h{t, u) on a probability space £2, we see the motivation for considering (1). Equation (2) then represents a nonlinear oscillati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2017
ISSN: 0170-4214
DOI: 10.1002/mma.4469