Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains [PDF]
, 2010 This is a survey of results mostly relating elliptic equations and systems of arbitrary even order with rough coefficients in Lipschitz graph domains.
Maz'ya, Vladimir, Shaposhnikova, Tatyana
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Decomposition theorem and Riesz basis for axisymmetric potenials in the right hal-plane [PDF]
, 2014 The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as $L_m[u]=\Delta u+\left(m/x\right)\partial_x u =0$, where $m\in\mathbb{C}$. We generalize results known for $m\in\
Chaabi, Slah, Rigat, Stephane
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Symmetry analysis of an acid-mediated cancer invasion model [PDF]
, 2022 Under investigation in this paper is a reaction-diffusion system, which describes acid-mediated tumor growth. First, in view of Lie group analysis, infinitesimal generators of the considered system are presented.
Ben Gao, Juya Cui
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Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition [PDF]
, 2010 International audienceThis work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is ...
Duran, Mario +2 more
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Boundary ellipticity and limiting $L^1$-estimates on halfspaces
, 2022 We identify necessary and sufficient conditions on $k$th order differential operators $\mathbb{A}$ in terms of a fixed halfspace $H^+\subset\mathbb{R}^n$ such that the Gagliardo--Nirenberg--Sobolev inequality $$ \|D^{k-1}u\|_{\mathrm{L}^{\frac{n}{n-1}
Gmeineder, Franz +2 more
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Primary ideals and their differential equations [PDF]
, 2020 An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE.
Cid Ruiz, Yairon +2 more
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On asymptotic effects of boundary perturbations in exponentially shaped Josephson junctions
, 2014 A parabolic integro differential operator L, suitable to describe many phenomena in various physical fields, is considered. By means of equivalence between L and the third order equation describing the evolution inside an exponentially shaped Josephson ...
De Angelis, Monica, Renno, Pasquale
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, 2013 In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order $1 \le \alpha \le 2$ is revisited. This equation interpolates between the diffusion and the wave equations that behave quite differently ...
Buckwar +34 more
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Right inverses for linear, constant coefficient partial differential operators on distributions over open half spaces [PDF]
, 1997 Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619 – 655 (1990)] are used to prove the following: Let and denote by its principal part.
Meise, Reinhold +2 more
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Partial Differential Equations in Applied MathematicsTime-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering ...
Md. Nur Alam, Md. Azizur Rahman
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