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Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods. [PDF]

J Math Biol
Lorenzi T, Painter KJ, Villa C.
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Classification of positive smooth solutions to third-order PDEs involving fractional Laplacians

Pacific Journal of Mathematics, 2018
This authors study a third-order conformal invariant equation with critical nonlinearity and a third-order critical static Hartree equation with nonlocal nonlinearity. By showing the equivalence between PDE and a integral equation, using some results in [\textit{W. Chen} et al., Commun. Pure Appl. Math. 59, No.
Dai, Wei, Qin, Guolin
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Qualitative properties of positive solutions to nonlinear pde and FBP

Nonlinear Analysis: Theory, Methods & Applications, 1996
The general goal of the paper is to study the qualitative properties of positive solutions of nonlinear divergence form elliptic equations \[ \nabla\cdot A(x,u,Du)+B(x,u,Du)=0,\quad x\in \Omega\subset\mathbb{R}^N,\quad N\geq 2. \] Applying the moving plane procedure of Aleksandrov, the author establishes star-shapedness of the level sets in certain ...
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Existence of a positive solution to a nonlinear system of PDEs in a domain with a triple-phase boundary

2013
We consider a system of nonlinear PDEs describing the reaction-diffusion dynamics near a triple-phase boundary in the catalyst layer of hydrogen fuel cells. The system involves bulk diffusion and surface reaction-diffusion processes and is an approximation of a model with a thin layer.
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Systemic therapy for hormone receptor‐positive/human epidermal growth factor receptor 2‐negative early stage and metastatic breast cancer

Ca-A Cancer Journal for Clinicians, 2023
Laura A Huppert, Hope S Rugo
exaly  

A method for constructing exact solutions of nonlinear delay PDEs

Journal of Mathematical Analysis and Applications, 2021
Andrei D Polyanin, Vsevolod G Sorokin
exaly  

Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy

Mathematics, 2021
Andrei D Polyanin, Vsevolod G Sorokin
exaly  

Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions

Mathematics, 2021
Alexander V Aksenov, Andrei D Polyanin
exaly