Related papers: Fully nonlinear parabolic equations in two space v…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…
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.
The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…
We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results…
The higher derivatives of the tangent and hyperbolic tangent functions are determined. Formulas for the higher derivatives of the inverse tangent and inverse hyperbolic tangent functions as polynomials are stated and proved. Using another…
We obtain an explicit H\"older regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor uniformly elliptic.
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
Using our results in [15], we provided existence theorems for the general classes of nonlinear evolutions. Finally, we give examples of applications of our results to parabolic, hyperbolic, Shr\"{o}dinger, Navier-Stokes and other…
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…
A notion of parabolic C-subsolutions is introduced for parabolic equations, extending the theory of C-subsolutions recently developed by B. Guan and more specifically G. Sz\'ekelyhidi for elliptic equations. The resulting parabolic theory…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a result has previously been studied only for certain…
We establish well-posedness and maximal regularity estimates for linear parabolic SPDE in divergence form involving random coefficients that are merely bounded and measurable in the time, space, and probability variables. To reach this…
Stabilization of equilibrium solution to parabolic like equations via proportional boundary feedbacks.
We are dealing with possibly degenerate second-order parabolic operators whose coefficients are infinitely differentiable with respect to space variables and only measurable with respect to the time variable. We impose the H\"ormander…