Self-similar solutions of the cubic wave equation
نویسندگان
چکیده
منابع مشابه
Signum-Gordon wave equation and its self-similar solutions
We investigate self-similar solutions of evolution equation of a (1+1)dimensional field model with the V-shaped potential U(φ) = |φ|, where φ is a real scalar field. The equation contains a nonlinear term of the form sign(φ), and it possesses a scaling symmetry. It turns out that there are several families of the self-similar solutions with qualitatively different behaviour. We also discuss a r...
متن کاملGlobal Infinite Energy Solutions for the Cubic Wave Equation
— We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
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 کاملBifurcations of self-similar solutions of the Fokker-Plank Equation
A class of one-dimensional Fokker-Plank equations having a common stationary solution, which is a power function of the state of the process, was found. We prove that these equations also have generalized self-similar solutions which describe the temporary transition from one stationary state to another. The study was motivated by problems arising in mathematical modeling of genome size evolution.
متن کاملThe Self-Similar Solutions of a Diffusion Equation
This paper discusses the diffusion equation with a damping term as follows ut = div(|Dum|p−2Dum)− u1 |Du|1 , where p > 2,m > 1, and p > p1, q1+p1m > m(p−1) > 1. By the standard Picard iteration method, a sufficient condition is given to the existence of the singular self-similar solutions. Moreover, the paper gives a classification for these singular self-similar solutions. Key–Words: Diffusion...
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: Nonlinearity
سال: 2010
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/23/2/002