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pro vyhledávání: '"35K55"'
We discuss a nonlinear system of partial differential equations modelling the formation of granuloma during tuberculosis infections and prove the global solvability of the homogeneous Neumann problem for \begin{align*} \begin{cases} u_t = D_u \Delta
Externí odkaz:
http://arxiv.org/abs/2411.00542
Autor:
Elliott, Charles M., Sales, Thomas
We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under
Externí odkaz:
http://arxiv.org/abs/2410.24147
Autor:
Andreucci, Daniele, Tedeev, Anatoli F.
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, roughly speaking of the type of the exponential of a power of the distance from the origin. We assume here the
Externí odkaz:
http://arxiv.org/abs/2410.23075
We consider a scalar parabolic partial differential equation on the interval with nonlinear boundary conditions that are asymptotically linear. As the parameter crosses critical values (e.g. the Steklov eigenvalues), it is known that there are large
Externí odkaz:
http://arxiv.org/abs/2410.22146
We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles that eith
Externí odkaz:
http://arxiv.org/abs/2410.15855
Autor:
Elbar, Charles
We prove $L^{\infty}_{t}W^{1,p}_{x}$ Sobolev estimates in the Keller-Segel system by proving a functional inequality, inspired by the Brezis-Gallou\"et-Wainger inequality. These estimates are also valid at the discrete level in the Jordan-Kinderlehre
Externí odkaz:
http://arxiv.org/abs/2410.15095
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density $\rho$ with a continuous and compactly supported nonlinear mobility $\mathrm{m}(\rho)$ not necessarily concave. The velocity field is the negative grad
Externí odkaz:
http://arxiv.org/abs/2410.10040
Autor:
Miura, Tatsuya
For a class of area-preserving curvature flows of closed planar curves, we prove that every immortal solution becomes asymptotically circular without any additional assumptions on initial data. As a particular corollary, every solution of zero enclos
Externí odkaz:
http://arxiv.org/abs/2410.06183
Autor:
Briozzo, Adriana C.
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary. Through s
Externí odkaz:
http://arxiv.org/abs/2410.03564
Publikováno v:
Discrete Continuous Dynamical Systems, Series B, 2019, V.24, p.3569-3590
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters \b{eta},{\
Externí odkaz:
http://arxiv.org/abs/2410.00457