Discrete and Continuous Dynamical Systems - Series S: latest papers http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=15 Latest articles for selected journal http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13954 Preface http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13954 PDE 2015 organized by H.-C. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, and E. Valdinoci at the Weierstrass Institute (WIAS) Berlin, November $30^\text{th}$ through December $4^\text{th}$, 2015.

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Hans-Christoph Kaiser, Dorothee Knees, Alexander Mielke, Joachim Rehberg, Elisabetta Rocca, Marita Thomas and Enrico Valdinoci Tue, 1 Aug 2017 20:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13955 Intrinsic geometry and De Giorgi classes for certain anisotropic problems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13955 Paolo Baroni, Agnese Di Castro and Giampiero Palatucci Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13956 The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13956 not $m$-sectorial. ]]> Jussi Behrndt and A. F. M. ter Elst Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13957 Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition -- The isothermal incompressible case http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13957 Dieter Bothe and Jan Prüss Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13958 Thermistor systems of $p(x)$-Laplace-type with discontinuous exponents via entropy solutions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13958 Miroslav Bulíček, Annegret Glitzky and Matthias Liero Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13959 Volume constrained minimizers of the fractional perimeter with a potential energy http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13959 Annalisa Cesaroni and Matteo Novaga Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13960 Characterizations of Sobolev functions that vanish on a part of the boundary http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13960 Moritz Egert and Patrick Tolksdorf Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13961 A survey on second order free boundary value problems modelling MEMS with general permittivity profile http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13961     The subsequent analytical investigations are restricted to a dissipation dominated regime for the membrane's displacement. For the resulting parabolic evolution problems local well-posedness, global existence, the occurrence of finite-time singularities, and convergence of solutions to those of the so-called small-aspect ratio model, respectively, are investigated. Furthermore, a topic is addressed that is of note not till non-constant permittivity profiles are taken into account -- the direction of the membrane's deflection or, in mathematical parlance, the sign of the solution to the evolution problem. The survey is completed by a presentation of some numerical results that in particular justify the consideration of the coupled problem by revealing substantial qualitative differences of the solutions to the widely-used small-aspect ratio model and the coupled problem. ]]> Joachim Escher and Christina Lienstromberg Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13962 Derivation of effective transmission conditions for domains separated by a membrane for different scaling of membrane diffusivity http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13962 Markus Gahn, Maria Neuss-Radu and Peter Knabner Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13963 On the geometry of the $p$-Laplacian operator http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13963 Bernd Kawohl and Jiří Horák Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13964 Effective acoustic properties of a meta-material consisting of small Helmholtz resonators http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13964 Agnes Lamacz and Ben Schweizer Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13965 On the existence of weak solutions of an unsteady $p$-Laplace thermistor system with strictly monotone electrical conductivities http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13965 Joachim Naumann Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13966 A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13966 Fabio Paronetto Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13967 An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13967 Tomáš Roubíček Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13968 Large solutions of parabolic logistic equation with spatial and temporal degeneracies http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13968 1$, $a(\cdot)$ is continuous, $b(\cdot)$ is continuous nonnegative function, satisfying condition: $b(t,x)≥ a_1(t)g_1(d(x))$, $d(x):=\textrm{dist}(x,\partial\Omega)$. Here $g_1(s)$ is arbitrary nondecreasing positive for all $s>0$ function and $a_1(t)$ satisfies: $$a_1(t)≥ c_0\exp(-\omega(T-t)(T-t)^{-1})\ \ \ \forall t < T,\ c_0=\textrm{const}>0$$ with some continuous nondecreasing function $\omega(\tau)≥0$ $\forall\tau>0$. Under additional condition: $$\omega(\tau)\rightarrow\omega_0=\textrm{const}>0\ \ \ \text{ as }\tau\rightarrow0$$ it is proved that there exist constant $k:0< k <\infty$, such that all solutions of mentioned equation (particularly, solutions, satisfying initial-boundary condition $u|_\Gamma=\infty$, where $\Gamma=(0,T)\times\partial\Omega\cup\{0\}\times\Omega$) stay uniformly bounded in $\Omega_0:=\{x\in\Omega:d(x) > k\omega_0^{\frac12}\}$ as $t\rightarrow T$. Method of investigation is based on local energy estimates and is applicable for wide class of equations. So in the paper there are obtained similar sufficient conditions of localization of singularity set of solutions near to the boundary of domain for equation with main part $P_0(u)=(|u|^{\lambda-1}u)_t-\sum_{i=1}^N(|\nabla_xu|^{q-1}u_{x_i})_{x_i}$ if $0 < \lambda ≤ q < p$. ]]> Andrey Shishkov Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13969 On the variational representation of monotone operators http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13969 representative function $f_\alpha: V \!\times\! V'\to \mathbb{R}\cup \{+\infty\}$ such that $$ f_\alpha(v,v') \ge \langle v',v\rangle \quad\;\forall (v,v'), \qquad\quad f_\alpha(v,v') = \langle v',v\rangle \;\;\Leftrightarrow\;\;\; v'\in \alpha(v).                   (0.1) $$ This provides a variational formulation for the above inclusions. Here we use this approach to prove two results of existence of a solution, without using the classical theory of maximal monotone operators. This is based on a minimax theorem, and on the duality theory of convex optimization. ]]> Augusto Visintin Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13970 The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13970 generalized Fisher information functional since it is obtained by autodissipation of another energy functional which generates the heat flow as its gradient flow with respect to the aforementioned distance. Our main results are twofold: For mobility functions satisfying a certain regularity condition, we show the existence of weak solutions by construction with the well-known minimizing movement scheme for gradient flows. Furthermore, we extend these results to a more general class of mobility functions: a weak solution can be obtained by approximation with weak solutions of the problem with regularized mobility. ]]> Jonathan Zinsl Tue, 1 Aug 2017 20:00:00 GMT