Teaching CSIR NET Mock Test Series Mathematical Science Partial Differential Equations Laplace Equation, Heat and Wave Equations
If u = (x, t) is the solution of the initial value problem
\(\left\{\begin{array}{ll} u_{t}=u_{x x}, & x \in \mathbb{R}, t>0 \\ u(x, 0)=\sin (4 x)+x+1, & x \in \mathbb{R} \end{array}\right.\)
satisfying |u(x. t)| < \(\rm 3e^{x^2}\) for all x ∈ ℝ and t > 0, then
1
\(\rm u\left(\frac{\pi}{8}, 1\right)+u\left(-\frac{\pi}{8},1\right)=2\)
2
\(\rm u\left(\frac{\pi}{8}, 1\right)=u\left(-\frac{\pi}{8},1\right)\)
3
\(\rm u\left(\frac{\pi}{8}, 1\right)+2u\left(-\frac{\pi}{8},1\right)=2\)
4
\(\rm u\left(\frac{\pi}{8}, 1\right)=-u\left(-\frac{\pi}{8},1\right)\)