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Existence of Weak Solutions to Nonlocal PDEs With a Generalized Definition of Caputo Derivative
Mediterranean Journal of Mathematics, 2023 Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we consider the existence of weak solutions to a kind of partial differential equations with Caputo ...
Xu, Jiaohui, Caraballo Garrido, Tomás
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On existence of a unique generalized solution to systems of elliptic PDEs at resonance [PDF]
Annales Polonici Mathematici, 2014 Tiantian Qiao +3 more
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Can There Be a General Nonlinear PDE Theory for Existence of Solutions? [PDF]
Reviews in Theoretical Science, 2015 Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the ...
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Известия Иркутского государственного университета: Серия "Математика", 2019 This paper is an attempt to give the review of a part of our results in the area of singular partial differential equations. Using the results of the theory of complete generalized Jordan sets we consider the reduction of the PDE with the irreversible ...
N.A. Sidorov
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Dispersionless integrable systems in 3D and Einstein-Weyl geometry [PDF]
, 2013 For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of ...
Ferapontov, Eugene, Kruglikov, Boris
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Nonlinear Waves: An Introduction [PDF]
, 2010 This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others ...
Popivanov, Petar, Slavova, Angela
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On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients
Journal of Applied Mathematics, 2013 We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values.
A. De Cezaro
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Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system [PDF]
, 2019 This manuscript extends the analysis of a much studied singularly perturbed three-component reaction-diffusion system for front dynamics in the regime where the essential spectrum is close to the origin.
Chirilus-Bruckner, Martina +3 more
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BSDE and generalized Dirichlet forms: the finite dimensional case [PDF]
, 2012 We consider the following quasi-linear parabolic system of backward partial differential equations: $(\partial_t+L)u+f(\cdot,\cdot,u, \nabla u\sigma)=0$ on $[0,T]\times \mathbb{R}^d\qquad u_T=\phi$, where $L$ is a possibly degenerate second order ...
Zhu, Rongchan
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, 2011 Following the previous works on the A. Pr\'astaro's formulation of algebraic topology of quantum (super) PDE's, it is proved that a canonical Heyting algebra ({\em integral Heyting algebra}) can be associated to any quantum PDE.
Prástaro, Agostino
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