Related papers: Quasilinear parabolic stochastic partial different…
We consider stochastic PDEs \[dY_t = L(Y_t)\, dt + A(Y_t).\, dB_t, t > 0\] and associated PDEs \[du_t = L u_t\, dt, t > 0\] with regular initial conditions. Here, $L$ and $A$ are certain partial differential operators involving…
In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDE where the coefficients satisfy a specific type Lyapunov condition instead of the classical coercivity condition. Moreover, based on…
We examine the stability of a class of quasilinear parabolic partial differential equations under perturbations. We are interested in the behavior of viscosity solutions as the perturbation parameter vanishes and establish explicit…
This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…
In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear…
In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for…
We study quasilinear parabolic stochastic partial differential equations with general multiplicative noise on a bounded domain in $\mathbb{R}^{d}$, with homogeneous Dirichlet boundary condition. We establish the existence and uniqueness of…
In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of…
In this paper, the existence and pathwise uniqueness of strong solutions for jump-type stochastic differential equations are investigated under non-Lipschitz conditions. A sufficient condition is obtained for ensuring the non-confluent…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the the unique continuation problem…
This paper establishes a new existence and uniqueness result of solutions for multidimensional backward stochastic differential equations (BSDEs) whose generators satisfy a weak monotonicity condition and a general growth condition in $y$,…
In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the…
This short note completes the symmetry analysis of a class of quasi-linear partial differential equations considered in the previous paper (Nonlinear Dynamics, Vol. 51, 309-316 (2008)): it deals with the presence of an "exceptional" Lie…
Regimes with a singular peaking for a wide class of quasilinear second order parabolic equations are studied. On the basis of energy methods, precise estimates of a final profile of a weak solution in a neighborhood of the peaking time are…
In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of…
We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic H\"older spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.
In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…