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This work is devoted to the nonexistence of global-in-time energy solutions of nonlinear wave equation of derivative type with weak time-dependent damping in the scattering and scale invariant range. By introducing some multipliers to…
The purpose of this article is to show that there are many differential viscoelastic models for which the global existence of a regular solution is possible. Although the problem of global existence in the classic Oldroyd model is still…
We shall be concerned with the Cauchy problem for quasilinear systems in three space dimensions of the form \label{i.1} \partial^2_tu^I-c^2_I\Delta u^I = C^{IJK}_{abc}\partial_c u^J\partial_a\partial_b u^K + B^{IJK}_{ab}\partial_a…
In this article we discuss the existence of local time for a class of Gaussian processes which appears as the solutions to some stochastic evolution equations. We show that on small intervals such processes are Gaussian integrators…
We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…
In this paper, we investigate a class of nonlinear impulsive stochastic differential evolution equations with infinite delay in Banach space. Based on the Krasnoselskii's fixed point theorem, sufficient conditions of the existence of the…
In this paper, we investigate the existence and finite-time blow-up for the solution of a reaction-diffusion system of semilinear stochastic partial differential equations (SPDEs) subjected to a two-dimensional fractional Brownian motion…
We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…
We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {\`a} la De Giorgi, as in…
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone…
An evidence of temporal dis-continuity of the solution in $F^s_{1, \infty}(\mathbb{R}^d)$ is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in…
This paper aims to study the relationship between the timelike extremal hypersurfaces and the classical minimal surfaces. This target also gives the long time dynamics of timelike extremal hypersurfaces in Minkowski spacetime…
This article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers equation perturbed by multiplicative white noise. The required results are obtained by stochastic…
We give sufficient conditions for global existence of positive mild solutions for the weak coupled system: \begin{eqnarray*} \frac{\partial u_{1}}{\partial t}…
In this paper we consider extended stationary mean field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean field…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…
This paper studies the long time stability of both stochastic heat equations on a bounded domain driven by a correlated noise and their approximations. It is popular for researchers to prove the intermittency of the solution which means…
A non-Gaussian Hardy equation is studied with a non-linearity of Osgood-type growth. A fractional derivative in time is incorporated for the first time in an research of this type. Existence of local and global solutions are established by…