The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications [PDF]
, 2008 This paper deals with a class of backward stochastic differential equations with Poisson jumps and with random terminal times. We prove the existence and uniqueness result of adapted solution for such a BSDE under the assumption of non-Lipschitzian ...
Mao, Xuerong +2 more
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Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach [PDF]
, 2022 [EN] In this article we study a class of Euler equations of compressible fluid dynamics. We give conditions under which the considered equations have at least one and at least two classical solutions.
Kheloufi, Arezki +3 more
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Existence of weak solutions for elliptic Dirichlet problems with variable exponent [PDF]
, 2023 summary:This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type $$ \begin{cases} -{\rm div} a(x, u, \nabla u)+b(x, u, \nabla u)=0 &\text {in} \ \Omega ,\\ u=0 &\text {on} \ \
Ri, Dukman, Kim, Sungchol
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Flows of singular vector fields and applications to fluid and kinetic equations [PDF]
, 2015 Several physical phenomena arising in fluid dynamics and kinetic equations can be modeled by nonlinear transport PDE. Such quantities are the vorticity of a fluid, or the density of a collection of particles advected by a velocity field which is highly ...
Bohun, Anna
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Applications of the Carathéodory theorem to PDEs [PDF]
, 2000 We discuss and exploit the Carathéodory theorem on existence and uniqueness of an absolutely continuous solution x: ℐ (⊂ ℝ) → X of a general ODE $ẋ {(*)\over=} ℱ(t,x)$ for the right-hand side ℱ : dom ℱ ( ⊂ ℝ × X) → X taking values in an arbitrary Banach ...
Konstanty Holly +3 more
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Regularity of minima: an invitation to the Dark Side of the Calculus of Variations [PDF]
, 2006 summary:I am presenting a survey of regularity results for both minima of variational integrals, and solutions to non-linear elliptic, and sometimes parabolic, systems of partial differential equations. I will try to take the reader to the Dark Side..
Mingione, Giuseppe, Giuseppe Mingione
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Weak solutions to stochastic differential equations driven by fractional Brownian motion [PDF]
, 2009 summary:Existence of a weak solution to the $n$-dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter $H\in (0,1)\setminus \{\frac 12\}$ is shown for a time-dependent but state-independent
Brzeźniak, Zdzisław +10 more
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper focuses on optimal design problems in the context of the Kirchhoff‐Love model for pure bending of a thin, solid, symmetric plate under a transverse load. The objective is to simultaneously determine the optimal outer shape of the domain and the distribution of two isotropic materials within the domain in order to minimize compliance.
Ivana Crnjac +2 more
wiley +1 more source
On the Global Asymptotic Stability of an Infection‐Age‐Structured Competitive Model
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We investigate an infection‐age‐structured competitive epidemiological model involving multiple strains. While classical results establish competitive exclusion when a unique maximal basic reproduction number exists, we provide here a complete characterization of the asymptotic behavior for an arbitrary number of populations without assuming ...
S. Girel, Q. Richard
wiley +1 more source
Well-posedness and qualitative properties of quasilinear degenerate evolution systems
, 2023 We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
Sonner, Stefanie, Mitra, Koondanibha
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