[EN] We consider the Cauchy problem for a general class of parabolic partial differential equations in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 0 such that, if the initial data f belongs to the closed linear span of e(n) with n >= n(m), then the decay rate of the solution of the problem is at least t(-m) for large times t. The result generalizes the recent study of the authors concerning the classical linear heat equation. We present variants of the result having different methods of proofs and also consider finite polynomial decay rates instead of unlimited m.The research of Bonet was partially supported by the projects MTM2016-76647P and GV Prometeo/2017/102 (Spain). The research of Taskinen wa...
International audienceWe consider existence and uniqueness issues for the initial value problem of p...
International audienceWe consider existence and uniqueness issues for the initial value problem of p...
We consider an abstract first order evolution equation in a Hilbert space in which the linear part i...
We consider the Cauchy problem for a general class of parabolic partial differential equations in th...
We consider the Cauchy problem for a general class of parabolic partial differential equations in th...
We consider the classical Cauchy problem for the linear heat equation and integrable initial data in...
We consider the classical Cauchy problem for the linear heat equation and integrable initial data in...
This paper is concerned with a Cauchy problem (P){ut=uxx−|u|p−1uinRx(0,∞),u(x,0)=u0(x)inR,, where p ...
AbstractWe characterize all domains Ω of RN such that the heat semigroup decays in L(L∞(Ω)) or L(L1(...
AbstractWe characterize all domains Ω of RN such that the heat semigroup decays in L(L∞(Ω)) or L(L1(...
AbstractWe study the large-time behavior of smooth solutions to a nonuniformly parabolic equation wi...
We consider an abstract first order evolution equation in a Hilbert space in which the linear part i...
We consider the second order Cauchy problem $$u_\epsilon''+u_\epsilon'+m{|A^1/2 u_\epsilon|}Au_\epsi...
23p.We consider a class of semi-linear dissipative hyperbolic equations in which the operator associ...
AbstractWe derive time-asymptotic decay rates in L2 for large disturbances to some important classes...
International audienceWe consider existence and uniqueness issues for the initial value problem of p...
International audienceWe consider existence and uniqueness issues for the initial value problem of p...
We consider an abstract first order evolution equation in a Hilbert space in which the linear part i...
We consider the Cauchy problem for a general class of parabolic partial differential equations in th...
We consider the Cauchy problem for a general class of parabolic partial differential equations in th...
We consider the classical Cauchy problem for the linear heat equation and integrable initial data in...
We consider the classical Cauchy problem for the linear heat equation and integrable initial data in...
This paper is concerned with a Cauchy problem (P){ut=uxx−|u|p−1uinRx(0,∞),u(x,0)=u0(x)inR,, where p ...
AbstractWe characterize all domains Ω of RN such that the heat semigroup decays in L(L∞(Ω)) or L(L1(...
AbstractWe characterize all domains Ω of RN such that the heat semigroup decays in L(L∞(Ω)) or L(L1(...
AbstractWe study the large-time behavior of smooth solutions to a nonuniformly parabolic equation wi...
We consider an abstract first order evolution equation in a Hilbert space in which the linear part i...
We consider the second order Cauchy problem $$u_\epsilon''+u_\epsilon'+m{|A^1/2 u_\epsilon|}Au_\epsi...
23p.We consider a class of semi-linear dissipative hyperbolic equations in which the operator associ...
AbstractWe derive time-asymptotic decay rates in L2 for large disturbances to some important classes...
International audienceWe consider existence and uniqueness issues for the initial value problem of p...
International audienceWe consider existence and uniqueness issues for the initial value problem of p...
We consider an abstract first order evolution equation in a Hilbert space in which the linear part i...