Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

The global-in-time existence of weak solutions to the barotropic compressible quantum
Navier–Stokes equations in a three-dimensional torus for large data is proved. The model …

Global existence and long-time behavior of solutions to a family of nonlinear fourth order
evolution equations on R d are studied. These equations constitute gradient flows for the …

We prove the global existence of non-negative variational solutions to the “drift diffusion”
evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under …

The logarithmic fourth-order equation \partial_tu+\frac12i,j=1^dij^2(uij^2\logu)=0, called the
Derrida–Lebowitz–Speer–Spohn equation, with periodic boundary conditions is analyzed …

In the manuscript, we are interested in using kinetic theory to better understand the time
evolution of wealth distribution and their large scale behavior such as the evolution of …

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion
systems modeling reversible chemical reactions under the detailed-balance condition. We …

A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth-order
DLSS equation in one space dimension is analyzed. The discretization is based on the …

This paper is motivated by the study of Lyapunov functionals for the Hele-Shaw and Mullins-
Sekerka equations describing free surface flows in fluid dynamics. We prove that the L2 …

We propose a method for numerical integration of Wasserstein gradient flows based on the
classical minimizing movement scheme. In each time step, the discrete approximation is …