相关论文: Global bifurcation for monotone fronts of elliptic…
In this paper we show global existence of Lipschitz continuous solution for the stable Muskat problem with finite depth (confined) and initial data satisfying some smallness conditions relating the amplitude, the slope and the depth. The…
We prove the existence of global solutions to the nonlinear wave equation in $\mathbb{R}^{1+3}$ $$\Phi_{tt} - \Delta \Phi \pm \Phi|\Phi|^{p-1} = 0$$ in the energy-supercritical regime $p>5$, for a class of large initial data. Our initial…
In this article we study topological bifurcations of critical orbits of equivariant gradient equations. We give necessary and sufficient conditions for the existence of global bifurcations of solutions of these equations. Moreover, we apply…
In this paper, we investigate the global behaviors of solutions to defocusing semilinear wave equations in $\mathbb{R}^{1+d}$ with $d\geq 3$. We prove that in the energy space the solution verifies the integrated local energy decay…
This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new…
We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary…
We describe how some differential geometric bifurcation problems can be treated with the MATLAB continuation and bifurcation toolbox pde2path. The basic setup consists in solving the PDEs for the normal displacement of an immersed surface…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler-Langevin-Korteweg system, which corresponds to the Euler-Korteweg system of compressible quantum fluids with an isothermal…
In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…
It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill--posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both…
In this paper, we propose a method of finding all coherent structures supported by a given nonlinear wave equation. It relies on enhancing the recent global bifurcation theory as developed by Dancer, Toland, Buffoni and others, by…
On strictly starshaped domains of second kind we find natural sufficient conditions which allow the solution of two long standing open problems closely related to the mean field equation $\prl$ below. On one side we catch the global…
We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth up to $\lambda_2+\delta$, examining in detail their behavior…
For domains of first kind [7,13] we describe the qualitative behavior of the global bifurcation diagram of the unbounded branch of solutions of the Gel'fand problem crossing the origin. At least to our knowledge this is the first result…
We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the…
In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
This paper considers a system modelling the evolution of a rigid body immersed in a bidimensional incompressible perfect fluid. In the special case of a disk-shaped rigid body, it was shown by C. Rosier and L. Rosier (2009) that the system…