Related papers: Global Solutions to the Discrete Nonlinear Breakag…
The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass…
We establish a non-explosion result for rough differential equations (RDEs) in which the noise and drift coefficients, together with their derivatives, may grow unboundedly at infinity. In addition, we prove the existence of a global…
The question of global existence or non-existence of solution to a given stochastic partial differential equation under some non-linear conditions always comes to mind. To show that our weak-predictable random field solutions do not have…
For regular and nonregular (singular) semilinear differential-algebraic equations (DAEs), we prove theorems on the existence and uniqueness of global solutions and on the blow-up of solutions, which allow one to identify the sets of initial…
We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence…
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…
The paper proves existence of mild solutions to normal discrete velocity Boltzmann equations sin the plane with no pair of colinear interacting velocities, and given ingoing boundary values. A key property is L1 compactness of the…
By using the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation, it is shown that there exists a global mild solution to the Cauchy problem for the relativistic Boltzmann equation with the assumptions of the…
On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing…
The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
This paper is devoted to the theoretical analysis of the nonlinear plate equations in $\mathbb{R}^{n}\times (0,\infty),$ $n\geq1,$ with nonlinearity involving a type polynomial behavior. We prove the existence and uniqueness of global mild…
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…
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…
A broad conjecture, formulated by the authors in earlier work, reads as follows: "Cubic defocusing dispersive one dimensional flows with small initial data have global dispersive solutions". Notably, here smallness is only assumed in $H^s$…
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in $D$-dimensional spacetime. These solutions are found by…
We prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an explicit counter-example that the linear growth condition is not…