heat equation with exponentially time dependent boundary condition











up vote
0
down vote

favorite
2












Consider the one dimensional heat equation on a semi-infinite bar such that



$u_t=u_{xx}$



with initial condition of



$u(x,0)=0$.



What is the solution for all x and t if the boundaries are



$u(0,t)=e^{-t}$
and
$u(x,t)=0$ as x approaches infinity?










share|cite|improve this question






















  • You must take the 'Laplace Transform of your equation' but, in that way, it's not clear hot to handle "$displaystylemathrm{u}left(x,tright) = 0$ as x approaches infinity".
    – Felix Marin
    Nov 14 at 16:58

















up vote
0
down vote

favorite
2












Consider the one dimensional heat equation on a semi-infinite bar such that



$u_t=u_{xx}$



with initial condition of



$u(x,0)=0$.



What is the solution for all x and t if the boundaries are



$u(0,t)=e^{-t}$
and
$u(x,t)=0$ as x approaches infinity?










share|cite|improve this question






















  • You must take the 'Laplace Transform of your equation' but, in that way, it's not clear hot to handle "$displaystylemathrm{u}left(x,tright) = 0$ as x approaches infinity".
    – Felix Marin
    Nov 14 at 16:58















up vote
0
down vote

favorite
2









up vote
0
down vote

favorite
2






2





Consider the one dimensional heat equation on a semi-infinite bar such that



$u_t=u_{xx}$



with initial condition of



$u(x,0)=0$.



What is the solution for all x and t if the boundaries are



$u(0,t)=e^{-t}$
and
$u(x,t)=0$ as x approaches infinity?










share|cite|improve this question













Consider the one dimensional heat equation on a semi-infinite bar such that



$u_t=u_{xx}$



with initial condition of



$u(x,0)=0$.



What is the solution for all x and t if the boundaries are



$u(0,t)=e^{-t}$
and
$u(x,t)=0$ as x approaches infinity?







heat-equation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 13 at 20:23









cat

11




11












  • You must take the 'Laplace Transform of your equation' but, in that way, it's not clear hot to handle "$displaystylemathrm{u}left(x,tright) = 0$ as x approaches infinity".
    – Felix Marin
    Nov 14 at 16:58




















  • You must take the 'Laplace Transform of your equation' but, in that way, it's not clear hot to handle "$displaystylemathrm{u}left(x,tright) = 0$ as x approaches infinity".
    – Felix Marin
    Nov 14 at 16:58


















You must take the 'Laplace Transform of your equation' but, in that way, it's not clear hot to handle "$displaystylemathrm{u}left(x,tright) = 0$ as x approaches infinity".
– Felix Marin
Nov 14 at 16:58






You must take the 'Laplace Transform of your equation' but, in that way, it's not clear hot to handle "$displaystylemathrm{u}left(x,tright) = 0$ as x approaches infinity".
– Felix Marin
Nov 14 at 16:58

















active

oldest

votes











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














 

draft saved


draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2997285%2fheat-equation-with-exponentially-time-dependent-boundary-condition%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes
















 

draft saved


draft discarded



















































 


draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2997285%2fheat-equation-with-exponentially-time-dependent-boundary-condition%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

Plaza Victoria

Puebla de Zaragoza

Musa