Related papers: Nonlinear enhanced dissipation in viscous Burgers …
This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…
We introduce a model for nonlinear viscoelastic solids where traveling shear waves with compact support are possible. We obtain an exact compact solution. We also derive a new Burger's type evolution equation associated with the introduced…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel…
This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the…
We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization,…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We propose a bulk viscous unified dark matter scenario based on a nonlinear extension of the full causal Israel-Stewart theory. This framework allows the viscous fluid to remain far from equilibrium, an essential feature for a physically…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
We develop a nonlinear generalisation of the causal linear thermodynamics of bulk viscosity, incorporating positivity of the entropy production rate and the effective specific entropy. The theory is applied to viscous fluid inflation (which…
The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
We develop a Lagrangian approach to conservation-law anomalies in weak solutions of inviscid Burgers equation, motivated by previous work on the Kraichnan model of turbulent scalar advection. We show that the entropy solutions of Burgers…
Differential equations with convective terms such as the Burger's equation appear in many applications and have been the subject of intense research. In this paper we use a generalized form of Cole-Hopf transformation to relate the…
We establish the vanishing viscosity limit of viscous Burgers-Vlasov equations for one dimensional kinetic model about interactions between a viscous fluid and dispersed particles by using compensated compactness technique and the evolution…
We study the non-diffusive Westervelt equation in the weakly nonlinear regime. We show that the leading profile equation is of Burgers' type. We show that a compactly supported nonlinearity $\alpha$ can be reconstructed from the tilt of the…
In this letter, a coupled system of viscous Burgers' equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgers' equation with zero Dirichlet boundary conditions,…
In this paper, we apply sensitivity methods to nonlinear PDEs like Burgers and KPZ equations. These equations are known to have analytical solutions which make easier the analysis of the sensitivity of their solutions to initial conditions.…
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the…
We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value…
We identify a class maximal dissipative solutions to models of compressible viscous fluids that maximize the energy dissipation rate. Then we show that any maximal dissipative solution approaches an equilibrium state for large times.