Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOptimal leading term of solutions to wave equations with strong damping terms
70
0
0.0
(
0
)
Authors
Hironori Michihisa
Ask ChatGPT about the research
No Arabic abstract
We analyze the asymptotic behavior of solutions to wave equations with strong damping terms. If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the Fourier space are obtained, which implies the optimality of expanding methods and some estimates proposed in this paper.
rate research
Read More
In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and those of heat equations can be seen by comparing the second order expansions of them. In order to analyze such effects we consider the weighted L1 initial data. We also give some lower bounds which show the optimality of obtained expansions.
We study the asymptotic behavior of solutions to wave equations with a structural damping term [ u_{tt}-Delta u+Delta^2 u_t=0, qquad u(0,x)=u_0(x), ,,, u_t(0,x)=u_1(x), ] in the whole space. New thresholds are reported in this paper that indicate which of the diffusion wave property and the non-diffusive structure dominates in low regularity cases. We develop to that end the previous authors research in 2019 where they have proposed a threshold that expresses whether the parabolic-like property or the wave-like property strongly appears in the solution to some regularity-loss type dissipative wave equation.
This paper is concerned with the initial value problem for semilinear wave equation with structural damping $u_{tt}+(-Delta)^{sigma}u_t -Delta u =f(u)$, where $sigma in (0,frac{1}{2})$ and $f(u) sim |u|^p$ or $u |u|^{p-1}$ with $p> 1 + {2}/(n - 2 sigma)$. We first show the global existence for initial data small in some weighted Sobolev spaces on $mathcal R^n$ ($n ge 2$). Next, we show that the asymptotic profile of the solution above is given by a constant multiple of the fundamental solution of the corresponding parabolic equation, provided the initial data belong to weighted $L^1$ spaces.
Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space translation, to a sum of solitary waves. This result is a consequence of a new general compactness/rigidity argument based on profile decomposition. We also give an application of this method to the energy-critical Schrodinger equation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
