相关论文: Regularity Analysis for an Abstract System of Coup…

The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs…

This paper is concerned with the study of regularity and stability properties of two Euler-Bernoulli beam equations with localized singular damping. Under suitable regularity assumptions on the damping coefficient, we establish Gevrey…

The paper concerned with higher order asymptotic expansion of solutions to the Cauchy problem of abstract hyperbolic equations of the form $u''+Au+u'=0$ in a Hilbert space, where $A$ is a nonnegative selfadjoint operator. The result says…

We obtained the $C^{\a}$ continuity for weak solutions of a class of ultraparabolic equations with measurable coefficients of the form ${\ptl_t u}= \sum_{i,j=1}^{m_0}X_i(a_{ij}(x,t)X_j u)+X_0 u$. The result is proved by simplifying and…

In this paper we study the weighted Gevrey class regularity of Euler equation in the whole space R 3. We first establish the local existence of Euler equation in weighted Sobolev space, then obtain the weighted Gevrey regularity of Euler…

In this paper, we shall recall and arrange the relationship between hyperbolic elements and parabolic subalgebras at first. And then, we shall classify all the compatible parabolic subalgebras containing a $\tau$-stable Borel subalgebra for…

We consider a class of weakly hyperbolic systems of first-order, nonlinear PDEs. Weak hyperbolicity means here that the principal symbol of the system has a crossing of eigenvalues, and is not uniformly diagonalizable. We prove the…

This paper studies H\"older regularity property of bounded weak solutions to a class of strongly coupled degenerate parabolic systems.

In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…

Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in…

In this paper, we show that, for scalar reaction-diffusion equations on the circle S1, the property of hyperbolicity of all equilibria and periodic orbits is generic with respect to the non-linearity . In other words, we prove that in an…

This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the velocity, and the velocities are less regular than the…

In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients.…

This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis…

We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…

We present a wave packet analysis of a class of possibly degenerate parabolic equations with variable coefficients. As a consequence, we prove local wellposedness of the corresponding Cauchy problem in spaces of low regularity, namely the…

We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…

We establish partial regularity for vector-valued solutions to parabolic systems where the coefficients are possibly discontinuous with respect to (x,t). More precisely, we assume a VMO-condition with respect to the (x,t) and continuity…

This paper studies the regularity of weak solutions to a class of parabolic perturbed fractional $1$-Laplace equations. Our analysis combines finite difference quotients, energy estimates, and iterative arguments, with a key step being the…

This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achieved for complexified problem with integral conditions…