capillary equation
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2016 ◽  
Vol 146 (5) ◽  
pp. 1017-1035 ◽  
Author(s):  
Rafael López

We obtain all the solutions of types u(x, y) = f(x) + g(y) and u(x, y) = f(x)g(y) for three known mean-curvature-prescribed equations, namely, the capillary equation, the translating soliton equation and the two-dimensional analogue of the catenary.


2016 ◽  
Vol 2016 ◽  
pp. 1-21
Author(s):  
B. Juarez Campos ◽  
Elena Kaikina ◽  
Hector F. Ruiz Paredes

We study the mixed initial-boundary value problem for the capillary wave equation:iut+u2u=∂x3/2u,  t>0,  x>0;  u(x,0)=u0(x),  x>0; u(0,t)+βux(0,t)=h(t),  t>0, where∂x3/2u=(1/2π)∫0∞sign⁡x-y/x-yuyy(y) dy. We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. Also we are interested in the study of the asymptotic behavior of solutions.


1996 ◽  
Vol 124 (2) ◽  
pp. 343-357 ◽  
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
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1975 ◽  
Vol 29 (2) ◽  
pp. 143-148 ◽  
Author(s):  
Paul Concus ◽  
Robert Finn

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