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A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

The partial differential equation u_t=u_(xxxxx)+5/2u_(xxx)u+(25)/4u_(xx)u_x+5/4u^2u_x.

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

An integer-relation algorithm which is based on a partial sum of squares approach, from which the algorithm takes its name.

Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar ...

The system of partial differential equations u_t+uu_x+vu_y=U_t+UU_x+mu/rhou_(yy) u_x+v_y=0.

The system of partial differential equations E_t-v = 0 (1) r_x+omegav = 0 (2) q_x+Ev = 0 (3) v_x-omegar-Eq = 0. (4)

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.