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Literatura académica sobre el tema "Equations d'évolution non locales en temps"
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Tesis sobre el tema "Equations d'évolution non locales en temps"
Nguyen, Thanh Nam. "Equations d'évolution non locales et problèmes de transition de phase". Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00919784.
Texto completoDannawi, Ihab. "Contributions aux équations d'évolutions non locales en espace-temps". Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS007/document.
Texto completoIn this thesis, we study four non-local evolution equations. The solutions of these four equations can blow up in finite time. In the theory of nonlinear evolution equations, a solution is qualified as global if it isdefined for any time. Otherwise, if a solution exists only on a bounded interval [0; T), it is called local solution. In this case and when the maximum time of existence is related to a blow up alternative, we say that the solution blows up in finite time. First, we consider the nonlinear Schröodinger equation with a fractional power of the Laplacien operator, and we get a blow up result in finite time Tmax > 0 for any non-trivial non-negative initial condition in the case of sub-critical exponent. Next, we study a damped wave equation with a space-time potential and a non-local in time non-linear term. We obtain a result of local existence of a solution in the energy space under some restrictions on the initial data, the dimension of the space and the growth of nonlinear term. Additionally, we get a blow up result of the solution in finite time for any initial condition positive on average. In addition, we study a Cauchy problem for the evolution p-Laplacien equation with nonlinear memory. We study the local existence of a solution of this equation as well as a result of non-existence of global solution. Finally, we study the maximum interval of existence of solutions of the porous medium equation with a nonlinear non-local in time term
Nabti, Abderrazak. "Non linear, non-local evolution equations : theory and application". Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS032.
Texto completoOur objective in this thesis is to study the existence of local solutions, existence global and blow up of solutions at a finite time to some nonlinear nonlocal Schrödinger equations. In the case when a solution blows-up at a finite time T < 1, we obtain an upper estimate of the life span of solutions. In the first chapter, we consider a nonlinear Schrödinger equation on RN. We first prove local existence of solution for any initial condition in L2 space. Then we prove nonexistence of a nontrivial global weak solution. Furthermore, we prove that the L2-norm of the local intime L2-solution blows up at a finite time. The second chapter is dedicated to study an initial value problem for the nonlocal intime nonlinear Schrödinger equation. Using the test function method, we derive a blow-up result. Then based on integral inequalities, we estimate the life span of blowing-up solutions. In the chapter 3, we prove nonexistence result of a space higher-order nonlinear Schrödinger equation. Then, we obtain an upper bound of the life span of solutions. Furthermore, the necessary conditions for the existence of local or global solutions are provided. Next, we extend our results to the 2 _ 2-system. Our method of proof rests on a judicious choice of the test function in the weak formulation of the equation. Finally, we consider a nonlinear nonlocal in time Schrödinger equation on the Heisenberg group. We prove nonexistence of non-trivial global weak solution of our problem. Furthermore, we give an upper bound of the life span of blowing up solutions
Belin, Théo. "On the free boundary of a forward-backward parabolic equation". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM040.
Texto completoIn this thesis, we focus on a forward-backward parabolic problem and the free boundary arising from it. The equation models a phase change driven by a Stefan problem coupled with a time nonlocal hysteresis operator. Our study deals with some theoretical and numerical aspects raised by this type of time nonlocal equation, in particular regarding the free boundary.First, we establish an equivalence between entropy inequalities associated with the problem and a weak formulation of the hysteresis operator. This discovery motivates the construction of a finite-volume numerical scheme whose convergence to a solution is shown. The compactness of the sequence of approximate solutions is based on Hilpert's inequality. Numerical experiments in dimensions 1 and 2 support these results and illustrate the behaviour of the free boundary.Next we establish a general framework of viscosity solutions for front propagation problems which are nonlocl in space and time. They may include a coupling with a bulk evolution equation. A strict comparison theorem and an existence theorem derived from Perron's method are proved. The Stefan problem and some variations of it fall within this general framework.Finally, motivated by the study of parabolic equations in time-varying domains appearing in couplings of front propagation problems, we prove new results of maximal regularity in Lebesgue spaces. Of particular interest is the precise estimation of the regularity constant for nonautonomous and relatively continuous operators. These results lead to new growth conditions guaranteeing the existence of strong global solutions to abstract quasi-linear problems on a bounded time interval
Nguyen, Thi Tuyen. "Comportement en temps long des solutions de quelques équations de Hamilton-Jacobi du premier et second ordre, locales et non-locales, dans des cas non-périodiques". Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S089/document.
Texto completoThe main aim of this thesis is to study large time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN in presence of an Ornstein-Uhlenbeck drift. We also consider the same issue for a first order Hamilton-Jacobi equation. In the first case, which is the core of the thesis, we generalize the results obtained by Fujita, Ishii and Loreti (2006) in several directions. The first one is to consider more general operators. We first replace the Laplacian by a general diffusion matrix and then consider a non-local integro-differential operator of fractional Laplacian type. The second kind of extension is to deal with more general Hamiltonians which are merely sublinear