Related papers: A priori estimates and theory of existence for par…
In this article, we prove a variety of uniqueness results for ultrahyperbolic equations with general space and time dependent lower order terms. We address the problem of determining uniqueness of solutions from boundary data as well as…
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.
We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many…
Regularity of solutions is studied for backward stochastic parabolic Ito equations. An analog of the second energy inequality and the related existence theorem are obtained for domains with boundary.
A priori estimates for finite-difference approximations for the first and second order derivatives are obtained for solutions of parabolic equations described in the title.
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.
Motivated by the study of certain non linear free-boundary value problems for hyperbolic systems of partial differential equations arising in Magneto-Hydrodynamics, in this paper we show that an a priori estimate of the solution to certain…
In this small paper, we study a boundary value problem for an equation of parabolic-hyperbolic type. The goal is to show how we can prove existence and uniqueness theorem for a regular solution.
In this paper we develop a geometric theory for quasilinear parabolic problems in weighted $L_p$-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a 3D viscous fluid…
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for its solutions over measurable sets.
We investigate the unique solvability of second order parabolic equations in non-divergence form in $W_p^{1,2}((0,T) \times \bR^d)$, $p \ge 2$. The leading coefficients are only measurable in either one spatial variable or time and one…
In this paper we study the degenerate parabolic $p$-Laplacian,$ \partial_t u - v^{-1}{\rm div}(|\sqrt{Q} \nabla u|^{p-2} Q \nabla u)=0$, where the degeneracy is controlled by a matrix $Q$ and a weight $v$. With mild integrability…
We consider variational problems with regular H{\"o}lderian weight or boundary singularity, and Dirichlet condition. We prove the boundedness of the volume of the solutions to these equations on analytic domains.
In this paper we give the explicit formulas for the solution of the singular generalized heat and wave equations on the Euclidian space $\R^n$.
Sufficient conditions for the well-posedness of the initial value problem for the scalar wave equation are obtained in space-times with hypersurface singularities
We prove that bounded weak solutions to degenerate parabolic double-phase equations of $p$-Laplace type are locally H\"older continuous. The proof is based on phase analysis and methods for the $p$-Laplace equation. In particular, the phase…
Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, $u_t = L(u_x)_x$, where $L$ is merely a monotone function. We also expose the basic properties of solutions,…