Blar i Institutt for matematiske fag på tidsskrift "Journal of Differential Equations"
Viser treff 1-14 av 14
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Competition models for plant stems
(Peer reviewed; Journal article, 2020)The models introduced in this paper describe a uniform distribution of plant stems competing for sunlight. The shape of each stem, and the density of leaves, are designed in order to maximize the captured sunlight, subject ... -
Dirichlet-to-Neumann maps, abstract Weyl–Titchmarsh M-functions, and a generalized index of unbounded meromorphic operator-valued functions
(Journal article; Peer reviewed, 2016)We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter dependent Dirichlet-to-Neumann maps associated to uniformly elliptic ... -
Exponential decay of solitary waves to Degasperis-Procesi equation
(Peer reviewed; Journal article, 2020)We improve the decay argument by Bona and Li (1997) [5] for solitary waves of general dispersive equations and illustrate it in the proof for the exponential decay of solitary waves to steady Degasperis-Procesi equation ... -
Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
(Peer reviewed; Journal article, 2023)We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa–Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time ... -
The Hunter-Saxton equation with noise
(Peer reviewed; Journal article, 2021)In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter–Saxton equation (1.1), and prove several properties of the blow-up of its solutions. An important part of the paper is the ... -
On fractional and nonlocal parabolic Mean Field Games in the whole space
(Peer reviewed; Journal article, 2021)We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional and anomalous diffusions in the whole space. These non-Gaussian diffusions are pure jump Lévy processes with some σ-stable like behaviour. ... -
On nonlocal quasilinear equations and their local limits
(Journal article, 2017)We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal ... -
On the Burgers–Poisson equation
(Journal article, 2016)In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 (R). In addition an Oleinik type estimate is established and some criteria on local ... -
One-sided Hölder regularity of global weak solutions of negative order dispersive equations
(Peer reviewed; Journal article, 2023)We prove global existence, uniqueness and stability of entropy solutions with initial data for a general family of negative order dispersive equations. These weak solutions are found to satisfy one-sided Hölder conditions ... -
Operator splitting for the Benjamin-Ono equation
(Journal article; Peer reviewed, 2015)In this paper we analyze operator splitting for the Benjamin–Ono equation, ut=uux+Huxx, where H denotes the Hilbert transform. If the initial data are sufficiently regular, we show the convergence of both Godunov and Strang ... -
Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations
(Peer reviewed; Journal article, 2020)In this work, we consider the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2\sigma}\partial_x u=0, \quad (t,x)\in \R\times \R. \end{align*} We prove ... -
Periodic Hölder waves in a class of negative-order dispersive equations
(Peer reviewed; Journal article, 2023)We prove the existence of highest, cusped, periodic travelling-wave solutions with exact and optimal α-Hölder continuity in a class of fractional negative-order dispersive equations of the form��+(|D|−��+�(�))�=0for every ... -
Symmetry and decay of traveling wave solutions to the Whitham equation
(Journal article, 2017)This paper is concerned with decay and symmetry properties of solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is ... -
Uniqueness of dissipative solutions for the Camassa-Holm equation
(Peer reviewed; Journal article, 2024)We show that the Cauchy problem for the Camassa–Holm equation has a unique, global, weak, and dissipative solution for any initial data u0 ∈H1(R), such that u0,x is bounded from above almost everywhere. In particular, we ...