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For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
The Becker-D\"oring equations are an infinite dimensional system of ordinary differntial equations describing coagulation/fragmentation processes of species of integer sizes. Formal Taylor expansions motivate that its solution should be…
We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the…
We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
Our main contributions include proving sufficient conditions for the existence of solution to a second order problem with nonzero nonlocal initial conditions, and providing a comprehensive analysis using fundamental solutions and…
The concept of weak invariants has recently been introduced in the context of conserved quantities in finite-time processes in nonequilibrium quantum thermodynamics. A weak invariant itself has a time-dependent spectrum, but its expectation…
Two-time correlations are a crucial tool to probe the dynamics of many-body systems. We use these correlation functions to study the dynamics of dissipative quantum systems. Extending the adiabatic elimination method, we show that the…
We prove optimal error bounds for a second order in time finite element approximation of curve shortening flow in possibly higher codimension. In addition, we introduce a second order in time method for curve diffusion. Both schemes are…
In this paper we study a class of semilinear wave type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able…
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
We consider the real-time evolution of a strongly coupled system of lattice fermions whose dynamics is driven entirely by dissipative Lindblad processes, with linear or quadratic quantum jump operators. The fermion 2-point functions obey a…
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For…
In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…
We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…
We consider the inverse problem of determining a time-dependent damping coefficient $a$ and a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+a(t,x)\partial_tu+q(t,x)u=0$ in $Q=(0,T)\times\Omega$, with…
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…