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Remarks on Nonlinear Evolution Equations
In the paper fully nonlinear evolution equations \[ {du \over dt} +A(t,u,u) = 0, \quad 0\leq t\leq T,\quad u(0) =\varphi, \] in a Banach space \(X\) are considered. Here \(T>0\), \(A\) is a nonlinear mapping of a subset \(D(A) \subset [0,T] \times X \times X\) into \(X\) and \(\varphi \in X\).
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Representations of sl(2,?) in category O and master symmetries [PDF]
We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such
J. P. Wang, Wang, Jing Ping
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The space–time fractional coupled modified equal-width equation and the coupled Boussinesq equation are a category of fractional partial differential equations, which might be crucial mathematical feathers in nonlinear optics, solid-state physics ...
M. Ayesha Khatun +4 more
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Many patients with urothelial cancer do not benefit from treatment with pembrolizumab, while at risk of severe side effects. Changes in the levels of circulating tumor DNA early during treatment, measured by a simple and affordable assay that can be easily implemented in the clinic, can be used as a prognostic tool to identify these patients.
Youssra Salhi +14 more
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In this article, a variety of solitary wave solutions are observed for microtubules (MTs). We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs ...
Md. Nur Alam, Md. Mahbub Alam
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The novel styrylquinazolinone‐based molecule W1B effectively suppresses glioblastoma by inhibiting IGF1R and EGFR. In high‐glucose microenvironments driving tumor resistance, W1B acts synergistically with the EGFR inhibitor dacomitinib. This combination safely blocks compensatory survival signaling in zebrafish xenograft models. Showcasing promising in
Patryk Rurka +9 more
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Controllability for a Nonlinear Abstract Evolution Equation
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Nonlinear Evolution Equations and Analyticity. I [PDF]
We prove a theorem on abstract nonlinear evolution equations ∂_tu = F(t, u) in a Banach space, which aims at estimating certain families of Liapunov functions for the solutions. The theorem is useful in proving global analyticity (in space variables) of solutions of various partial ...
Kato, Tosio, Masuda, Kyûya
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Enzymes of the 2‐hydroxyacyl‐CoA lyase group catalyze the condensation of formyl‐CoA with aldehydes or ketones. Thus, by structural adaptation of active sites, practically any pharmaceutically and industrially important 2‐hydroxyacid could be biotechnologically synthesized. Combining crystal structure analysis, active site mutations and kinetic assays,
Michael Zahn +4 more
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On the optimal control of strongly nonlinear evolution equations
In this paper we study optimal control problems governed by nonlinear evolution equations with nonmonotone nonlinearities in the state. First we prove an existence theorem. Then using the penalty method we obtain necessary conditions for optimality. From
Papageorgiou, Nikolaos S +1 more
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