1,721,004 research outputs found
Existence of solutions for some non-Fredholm integro-differential equations with mixed diffusion
No full textWe establish the existence in the sense of sequences of solutions for certain integro-differential type equations in two dimensions involving the normal diffusion in one direction and the anomalous diffusion in the other direction in H-2(R-2) via the fixed point technique. The elliptic equation contains a second order differential operator without the Fredholm property. It is proved that, under the reasonable technical conditions, the convergence in L-1(R-2) of the integral kernels implies the existence and convergence in H-2(R-2) of the solutions. (C) 2021 Elsevier Inc. All rights reserved
Symmetrization and stabilization of solutions of nonlinear elliptic equations
No full textThis book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists
SOLVABILITY OF SOME INTEGRO-DIFFERENTIAL EQUATIONS WITH DRIFT
Get PDFWe prove the existence in the sense of sequences of solutions for some integro-differential type equations involving the drift term in the appropriate H² spaces using the fixed point technique when the elliptic problems contain second order differential operators with and without Fredholm property. It is shown that, under the reasonable technical conditions, the convergence in L¹ of the integral kernels yields the existence and convergence in H² of solutions
Continuous dependence on a parameter of exponential attractors for chemotaxis-growth system
Get PDFWe study dependence on a parameter of exponential attractors. As known, exponential attractors are not uniquely determined from a dissipative dynamical system even if they exist. But we prove in this paper that one can construct an exponential attractor which depends continuously on a parameter in the dynamical system. This result is then applied to the chemotaxisgrowth system
SOLVABILITY OF SOME INTEGRO-DIFFERENTIAL EQUATIONS WITH DRIFT
No full textWe prove the existence in the sense of sequences of solutions for some integro-differential type equations involving the drift term in the appropriate H² spaces using the fixed point technique when the elliptic problems contain second order differential operators with and without Fredholm property. It is shown that, under the reasonable technical conditions, the convergence in L¹ of the integral kernels yields the existence and convergence in H² of solutions
Mathematical modeling of mitochondrial swelling
No full textThe mathematical models considered in this book can help to understand the swelling of mitochondria. For the first time, it presents new mathematical models of mitochondrial swelling that take into account, in particular, spatial effects. The results presented here could make it possible to predict properties of the underlying biological mechanisms. Taking into account that mitochondria could move within a cell, lead to a PDE-PDE model. The book discusses the well-posedness and long-term dynamics of solutions, depending on boundary conditions reflecting the in vitro and in vivo cases. These analytical and numerical results have inspired colleagues from the Institute of Pharmacology and Toxicology of the Helmholtz Center Munich to design new experiments justifying the theoretical and numerical results that are obtained. The book is intended for graduates students and researchers with a solid mathematical background and an interest in cell biology
Classification of Existence and Non-Existence of Running Fronts in Case of Fast Diffusion
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