Trace theory for parabolic boundary value problems with rough boundary conditions [0.03%]
粗糙边界条件下抛物型边值问题的迹理论
Robert Denk,Floris B Roodenburg
Robert Denk
We characterize the trace spaces arising from intersections of weighted, vector-valued Sobolev spaces, where the weights are powers of the distance to the boundary. These weighted function spaces are particularly suitable for treating bound...
Existence of variational solutions to doubly nonlinear systems in nondecreasing domains [0.03%]
非降域上双重非线性系统的变分解的存在性
Leah Schätzler,Christoph Scheven,Jarkko Siltakoski et al.
Leah Schätzler et al.
For q ∈ ( 0 , ∞ ) , we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form ∂ t ( | u | q - 1 u ) - div ( D ξ f ( x , u , D u ) ) = - D u f ( x , u , D u ) in a bounded noncylindr...
Christa Cuchiero,Tonio Möllmann,Josef Teichmann
Christa Cuchiero
Generalized Feller theory provides an important analog to Feller theory beyond locally compact metric state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional proces...
A Alexandrou Himonas,Fangchi Yan
A Alexandrou Himonas
The well-posedness of the initial-boundary value problem for higher-order quadratic nonlinear Schrödinger equations on the half-line is studied by utilizing the Fokas solution formula for the corresponding linear problem. Using this formul...
Well-posedness of Keller-Segel systems on compact metric graphs [0.03%]
关于紧致度量图上的Keller-Segel系统的适定性问题
Hewan Shemtaga,Wenxian Shen,Selim Sukhtaiev
Hewan Shemtaga
Chemotaxis phenomena govern the directed movement of microorganisms in response to chemical stimuli. In this paper, we investigate two Keller-Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks. The ...
On the Weierstraß form of infinite-dimensional differential algebraic equations [0.03%]
无限维微分代数方程的魏尔斯特拉斯标准型
Mehmet Erbay,Birgit Jacob,Kirsten Morris
Mehmet Erbay
The solvability for infinite-dimensional differential algebraic equations possessing a resolvent index and a Weierstraß form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which solutions e...
The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture [0.03%]
非线性Kelvin-Voigt型动态断裂模型中的粘弹性悖论问题
Maicol Caponi,Alessandro Carbotti,Francesco Sapio
Maicol Caponi
In this paper, we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a s...
Existence and convergence of the length-preserving elastic flow of clamped curves [0.03%]
固定端点曲线长度守恒弹性流的存在性与收敛性
Fabian Rupp,Adrian Spener
Fabian Rupp
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative L 2 -gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoo...
Weak and parabolic solutions of advection-diffusion equations with rough velocity field [0.03%]
带粗糙速度场的对流扩散方程的弱解和奇性扩散方程的解
Paolo Bonicatto,Gennaro Ciampa,Gianluca Crippa
Paolo Bonicatto
We study the Cauchy problem for the advection-diffusion equation ∂tu+div(ub)=Δu associated with a merely integrable divergence-free vector field b defined on the torus. We discuss existence, regularity and uniqueness results for ...
Lorenzo Dello Schiavo,Melchior Wirth
Lorenzo Dello Schiavo
We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Fur...