Global existence and time-decay rates of solutions to the generalized Boussinesq equation with weak damping
نویسندگان
چکیده
In this paper, we study the initial value problem for generalized Boussineq equation with weak damping. The existence and time-decay rates of global solutions its derivatives are established all space dimensions d ≥ 1, provided that norm data is suitably small. negative Sobolev norms in low frequency shown to be preserved along time evolution enhance decay solutions. proof based on energy method flexible interpolation trick without investigating corresponding linear equation.
منابع مشابه
Existence and Decay Rates of Solutions to the Generalized Burgers Equation
In this paper we study the generalized Burgers equation ut + (u /2)x = f(t)uxx, where f(t) > 0 for t > 0 . We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to L∞(R), as well it is obtained the decay rates of u in L norm are algebra order for p ∈ [1,∞[.
متن کاملGlobal Existence of Weak Solutions for the Burgers-Hilbert Equation
This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L(IR). For positive times, the solution lies in L2∩L∞. A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.
متن کاملDecay estimates of solutions to the IBq equation
In this paper we focus on the Cauchy problem for the generalized IBq equation with damped term in $n$-dimensional space. We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value, provided that the initial value is suitably small. Moreover, we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...
متن کاملGlobal Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.
متن کاملExistence, global nonexistence, and asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation
where u (x, t) denotes the unknown function, f (s) is the given nonlinear function, u0 (x) and u1 (x) are the given initial value functions, k is a constant, the subscript t indicates the partial derivative with respect to t, n is the dimension of space variable x, and △ denotes the Laplace operator in R. The effects of small nonlinearity and dispersion are taken into consideration in the deriv...
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: Journal of Mathematical Physics
سال: 2023
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0135436