Zobrazeno 1 - 10
of 123
pro vyhledávání: '"35G10"'
Autor:
Kim, Taehun
We provide a set of conditions that is necessary and sufficient for the $L^{2}$-wellposedness of the Cauchy problem for fifth and sixth order variable-coefficient linear dispersive equations. The necessity of these conditions had been presented by Ta
Externí odkaz:
http://arxiv.org/abs/2410.15104
Autor:
Memana, Gautam Neelakantan
We prove a sharp interior regularity theorem for fully nonlinear maximally subelliptic PDE in non-isotropic Sobolev spaces adapted to maximally subelliptic operators. This result complements the regularity theorem proven by Street for adapted Zygmund
Externí odkaz:
http://arxiv.org/abs/2409.04344
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$ large, we p
Externí odkaz:
http://arxiv.org/abs/2407.18630
Autor:
Hopkalo, Olha, Sakhno, Lyudmyla
The paper presents bounds for the distributions of suprema for a particular class of sub-Gaussian type random fields defined over spaces with anisotropic metrics. The results are applied to random fields related to stochastic heat equations with frac
Externí odkaz:
http://arxiv.org/abs/2405.04242
Publikováno v:
Partial Differential Equations in Applied Mathematics 2024 Volume 9 (short version)
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a generalization o
Externí odkaz:
http://arxiv.org/abs/2405.03383
Our aim in this paper is to discuss the critical exponent in semi-linear structurally damped wave and beam equations with additional dispersion term. The special model we have in mind is $$ u_{tt}(t,x)+(-\Delta)^{\sigma}u(t,x)+(-\Delta)^{2\delta}u(t,
Externí odkaz:
http://arxiv.org/abs/2404.01544
Autor:
Li, Xiaoyan, Ikehata, Ryo
We report that the quantity measured in the $L^2$ norm of the solution itself of the generalized Rosenau equation, which was completely unknown in this equation, grows in the proper order at time infinity. It is also immediately apparent that this gr
Externí odkaz:
http://arxiv.org/abs/2311.01027
Autor:
Junior, Alexandre Arias
We consider the Cauchy problem for Schr\"odinger type operators. Under a suitable decay assumption on the imaginary part of the first order coefficients we prove well-posedness of the Cauchy problem in Gelfand-Shilov classes. We also discuss the opti
Externí odkaz:
http://arxiv.org/abs/2309.08194
In this paper we consider a class of $p$-evolution equations of arbitrary order with variable coefficients depending on time and space variables $(t,x)$. We prove necessary conditions on the decay rates of the coefficients for the well-posedness of t
Externí odkaz:
http://arxiv.org/abs/2309.05571
Necessary and sufficient conditions on a family of integro-differential operators to determine a formal automorphism are established. Equivalently, the problem can be read in terms of existence and uniqueness of formal solutions of Cauchy problems in
Externí odkaz:
http://arxiv.org/abs/2306.06398